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In his 1989 book ''Crazy English'' (Pocket Books, ISBN 0-671-68907-X),
Richard Lederer calls such words and phrases "contronyms" and lists
41.  This phenomenon has been a curiosity to users of language for
as long as there has been language and has many names:

  addad (Arabic)
  antilogy
  antiphrasis
  auto-antonymy
  didh (Arabic)
  enantiodromia (Greek)
  enantiosemy (Greek)
  enantiosis (Greek)
  gegensinn (German)
  Janus words
  l'shon hefech (Hebrew)
  mirror words
  oysterisms
  polarity
  self-antonymy
  turncoat words

Such words can be divided into homographs (same spelling) and
homophones (same pronunciation).

A very short list of homophones:
 aural, oral = heard, spoken
 enumerable, innumerable = countable, uncountable
 erupt, irrupt = burst out, burst in
 eradicate, irradicate = pull up by the roots, root deeply
 fiance, fiancee = female betrothed, male betrothed
 raise, raze = erect, tear down
 reckless, wreckless = careless, careful
 succor, sucker = aid, hoodwink

A partial list of homographs:
 aboard = alongside, inside
 against = in the direction of and in contact with, in an opposite direction
 all downhill from here = things are going to get better, things are going to  get worse
 aloha = hello, goodbye
 anabasis = military advance, military retreat
 anathema = something cursed, [[[rare]] something consecrated to divine use
 anon  = immediately [[[archaic]] or soon, later
 anxious = full of mental distress because of apprehension of danger or misfortune [[[in effect, seeking to avoid]] (We were anxious about the near by gunshots.), eager or looking forward to (until you returned, I was anxious to see you.)
 apparent = not clear or certain (for now, he is the apparent winner of the contest.), obvious (The solution to the problem was apparent to all.)
 apparent = seeming, clear ("heir apparent")
 argue = to try to prove by argument, [[[disputed]] to argue against
 arsis = the unaccented or shorter part of a foot of verse; the accented or longer part of a foot of verse
 assume = to actually have (to assume office), to hope to have ("he assumed he would be elected.")
at the expense of = by sacrificing ("at the expense of accuracy"), [[disputed]] by tolerating or introducing ("at the expense of inaccuracy")
 aught = all, nothing
 ave = hail, farewell
 avocation = a hobby, a regular occupation [[and one could say it's a triple   antagonym if you agree that the archaic meaning of "a distraction" is the opposite of working (even at a hobby) and if you agree that the obsolete meaning of "a calling away" takes you away from (the opposite of participating in) your hobbies, work, and even your distractions====]]
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 awful = extremely unpleasant, ugly, awe-inspiring [[typically, a feeling of admiration]]
 bad = of poor quality, [[[U.S. slang]] good
 barrack = root or cheer, [[[Australian]] jeer or heckle
 below par = good (in golf), bad (in health)
 bill = money, statement of money owed
 bimonthly/weekly = twice a month/week, once every two months/weeks
 bolt = to secure in place, to dart away
 bomb = [[[U.S. slang]] a failure, [[[U.K. slang]] a success
 bound = moving ("I was bound for Chicago"), unable to move ("I was bound to a post", or less literally, "I was bound to my desk")
 buckle = to hold together (e.g. buckle your belt), to fall apart (e.g., buckle under pressure)
 bull = a solemn edict or mandate, nonsense or worthless information
 by = spoken representation of multiplication sign ("3-by-3 matrix"), spoken representation of division sign ("d y by d x")
 cakewalk = easy task, intricate walk contest
cannot praise too highly = no praise is too high, cannot praise very highly
 certain = definite, hard to specify ("I have a certain feeling.")
 charter = grant for pay, use for pay
 cheerio = hello, goodbye
 chine = ridge, [[[British dialect]] ravine
 chuffed = [[[slang]] pleased, [[[slang]] annoyed
 cipher = zero, any number
 cite, citation = for doing good (such as military gallantry), for doing bad  (such as from a traffic policeman)
 cleave = to separate, to join
 clip = cut apart, fasten together
 cognomen = first name, last name
 commencement = beginning, [[[disputed]] conclusion ("high school commencement")
 comprise = to contain entirely ("the United States comprises 50 states"), to  be included in ("The 50 states comprise the United States" )
 consult = to ask the advice of, to give professional advice
 contingent = unpredictable, dependent on a known condition
 continue = proceed with, [[[US & Scottish legal usage]] postpone
 cool = positive sense (cool web-sites), negative sense (cool reception)
 copemate = antagonist, partner
 could care less = (used as if it were synonymous with "could not care less"), one has no interest at all
 counterfeit = [[[archaic]] a legitimate copy, a copy meant to deceive
 critical = opposed to ("critical of"), essential to ("critical to")
 custom = [[[noun]] usual, [[[adjective]] special
 cut = to get in ("cut line"), to get out ("cut class")
 deceptively <any adjective> = more <any adjective> than it looks, less ...
 dike = wall, ditch
 discursive = moving from topic to topic without order, proceeding coherently  from topic to topic
 dispense with = distribute with, do without (We dispense with accuracy.)
 dispose of = to place in an orderly way, to get rid of
 divide by a half = to double, [[[disputed]] to halve
 dollop = a large amount, [[[U.S.]] a small amount
 down = hill, valley
 downhill = easy, progressively worse
 dress = put covering (usu. clothes) on, take covering (usu. skin) off
 dust = to remove dust, to apply dust (as in fingerprinting)
 edited = remaining after omissions have been made, [[disputed]] omitted
 effectively = in effect (doing the equivalent of the action but not the real  thing), with effect (doing the action and doing it well) [[Contrast "he is effectively lying" (colloquial?) with "he is lying effectively"]]
 egregious = outstandingly bad, [[[archaic]] distinguished
 enervate = to deplete the energy of, [[[disputed]] to invigorate
 enjoin = to order someone to do something, to stop someone from doing  something [[[such as in law by an injunction]]
 factoid = speculation reported as fact, [[[disputed]] unimportant fact
 fast = moving rapidly, unable to move ("I was held fast to my bed.")
 fearful = causing fear, being afraid
 finish = kill, perfect (at a finishing school)
 fireman = firefighter, fire-stoker (on train or ship)
 first-degree = most severe ("first-degree murder"), least severe ("first- degree burns")
  fix = to restore to function (fixing the refrigerator), to make non-functional (fixing the dog)
 flesh = add body matter, remove body matter
 flog = to criticize harshly, to promote aggressively
 for sure = certainly, [[[slang]] certainly not
 fought with = fought on the same or opposite sides (The Finns fought with the Germans in WW II.)
 gale = a very strong wind, [[[archaic]] a gentle breeze
 garble = to mix up, [[[archaic]] to sort out
 garnish = to add to food, to subtract from wages
 gaum = to understand, to act stupid
 give out = to produce, to stop being produced
 go off = to become active, to become inactive
 good deal = [[[disputed]] very much (expensive), very little (bargain)
 goods = [[[slang]] good things, bad things ("I have the goods from the warehouse  robbery, but I'm worried the police have the goods on me.")
 grade = an incline, level ("grade crossing")
 handicap = advantage (in golf), disadvantage
 help = to assist, to prevent ("I cannot help it if...")
 hoi polloi = the common people, [[disputed]] the elite
 hold up = to support, to delay
 homely = [[[US]] ugly, [[[UK]] pleasant
 hysterical = being overwhelmed with fear [[in some cases]], being funny
 impregnable = invulnerable, [[[disputed]] impregnatable
 impugnable = able to be impugned, [[[obsolete]] impregnable
 incorporate = when a village is incorporated, it is formed, but when it is  incorporated into a city, the village is destroyed
 inexistent = inherent, [[[obsolete]] nonexistent
 infer = to take a hint, [[[disputed]] to hint
 inside lane = [[[US]] lane nearest center, [[[UK]] lane nearest edge
 into = as a divisor of, [[[in India]] multiplied by
 jake = [[[[disputed]] uncouth (person), fine
 keep up = to continue to fall (rain), [[[disputed]] to remain up
 kick off = begin, die
 last = just prior, final (my last book will be my last publication)
 lease = become lessor, become lessee
 left = departed from ("He left."), remaining ("He was left.")
 let = to permit, [[[archaic]] to hinder
 license = liberty or permission to do something, undue or excessive freedom  or liberty
 like never before = totally amateurish, with great skill (she's dancing like she's never danced before.)
 literally = actually, [[[disputed]] figuratively (used before a metaphor)
 livid = discolored by bruising, pale
 look out for = be afraid of, anticipate
 lurch = run away, walk aimlessly
 mad = carried away by enthusiasm or desire, carried away by hatred or anger
 mark = write, read ("mark my words")
 mean = lowly ("rose from mean beginnings"), excellent ("plays a mean  trombone")
 model = archetype, copy
 moot = debatable, [[[disputed]] not worthy of debate
 mortal = receiver of death, giver of death ("He dealt a mortal blow.")
 mortar = glue together, blow apart
 mosey = run away, walk aimlessly
 nauseous = nauseating, [[[disputed]] nauseated
 near miss = a hit close enough to achieve the effect, narrowly falling short  of the objective
 nervy = showing calm courage, excitable
 note = promise to pay, money
 out = invisible (Turn the lights out.), visible (The moon is out.)
 out of = outside, inside ("work out of one's home")
 overlook = inspect, ignore
 oversight = care, error
 peep = to look quietly, to beep
 peer = noble, person of equal rank
 peruse = examine in detail, look over casually
 pitch = erect and fix firmly in place, throw away
 poke your head = make head poker, make head pokee
 policy = required activity without exception (university policy), an optional course of action (our government's policy regarding the economy)
 populate = to decimate the population (obsolete use), to increase the population
 practiced = [[[adjective]] expert, [[[verb]] inexpertly attempted
 prescribe = to lay down a rule, to become unenforceable
 presently = in a little while, [[[archaic]] immediately
 priceless = have a very high value, having no market value
public school = [[[US]] tax-supported school, [[[UK]] endowed school
 put = lay, throw
 put out = to generate ("candle puts out light"), to extinguish
 put up = set up, take down ("Put up your toys.")
 puzzle = to pose a problem, to solve a problem
 quaint = beautiful, odd
 qualified = competent, limited ("The dance was a qualified success.")
 quantum = very small ("quantum level"), [[[disputed]] very large ("quantum leap")
 quiddity = an inessential feature, the essence
 quite = rather, completely
 ravel = to disentangle, [[[archaic]] to tangle
 recover = hide away (cover again), bring out [[[hyphenated as re-cover]]
 referent = something referred to, [[[disputed]] something referring to
 refrain = [[[music]] repeat a certain part, stop
 release = let go, hold on [[[hyphenated as re-lease]]
 rent = to buy temporary use of, to sell temporary use of
 replace = take away (replace the worn carpet), put back (replace the papers in the file)
 repress = hold back, put forth (press again) [[[hyphenated as re-press]]
 reprove = rebuke (reprove a colleague's work), support [[[hyphenated as re-prove]]
 reservation = what you make when you know where you want to go, what you have when you're not sure if you want to go
 reside = to stay put, [[[slang]] to change places (change teams) [[[hyphenated as re-side]]
 resign = to quit a contract, to sign the contract again [[[hyphenated as re-sign]]
 restive = refusing to move ("a restive horse"), restless
 reword = to repeat in different words, [[[archaic]] to repeat in the same words
 riot = violent disorder, revelry ("It was a riot====")
====
 rival = an opponent, [[[archaic]] a companion or associate
 rocky = firm, steadfast, tending to sway (e.g., a rocky shelf)
 root = to establish (The seed took root.), to remove entirely (Root out  dissenters)
 rummage = thoroughly search, haphazardly search
 sanction = to approve of, [[[disputed]] to punish
 sanguine = hopeful, [[[obsolete for "sanguinary"]] murderous
 scan = to examine closely, to look over hastily
 scary = causing fright, easily scared
 screen = to show, to hide from view
 screwed = [[[slang]] to be taken advantage of, to fool around and have fun
 secrete/d = to extrude, to hide
 seed = remove the seeds, distribute the seeds
 seeded = with seeds, without seeds
 set = bend, make unyielding; become established, come to an end (the era sets)
 shalom = hello, farewell
 shank of the evening = end of the evening, early part of the evening
 shop = to search with the intent to buy, to search with the intent to sell  ("I shopped my manuscript to several publishers.")
 sick = unpleasant (a sick joke), [[[slang]] wonderful
 siren = seductive sound, harsh sound
 skin = to cover with a skin, to remove outer covering or skin
 speak = express verbally, [[[disputed]] express nonverbally
 stain = color, discolor
 stamp out = eliminate, produce in great quantities
 stipulate = request explicitly, agree to
 straight = not using drugs, [[[obsolete]] under the influence of drugs
 strand = shore, [[[Scots]] sea
 strike = to miss (baseball), to hit
 strike out = an ending ("The batter struck out."), a beginning ("I struck out on my own.")
 substitute = to put (something) in something else's place, [[[disputed]] to  replace (something) with something else
 tabby = a silk fabric, a rough kind of concrete
 table = [[[UK]] to propose, [[[US]] to set aside
 take = obtain, offer ("Models take good pictures.")
 take care of = look out for and nurture, [[[slang]] get rid of or kill
 take fire = withstand fire, be ignited
 tell me about it = I want to know more, I already know
 temper = calmness, passion; harden (steel), soften (justice)
 terrific = extraordinarily good, causing terror
 thesis = [[[poetics]] accented part, unaccented part
 think better of = to admire more, to be suspicious of
 through = [[[US]] finished, [[[UK]] connected (telephone)
 tilt = to incline toward, to charge against
 to a degree = [[[archaic]] exceedingly, [[[disputed]] to a certain extent
 to my knowledge = to my certain knowledge, as far as I know
 toast = popular ("the toast of the town"), [[[US slang]] doomed
 transparent = obvious, invisible
 trim = to put things on ("trim a Christmas tree"), to take things off
 trip = to stumble, to move gracefully ("trip the light fantastic")
 tropics = area near equator, limits of this area
 turn it up = [[[US]] increase volume, [[[UK]] cease
 unbending = rigid, relaxing ("Learn to unbend.")
 undersexed = having a lower-than-normal sex drive, [[[disputed]] sexually  deprived
 unqualified = not qualified, very qualified ("He was an unqualified success.")
 vernacular = nonstandard speech, standard speech
 vital = lively, deadly
 watch out for = be afraid of, anticipate
 watershed = the divide between regions drained by different rivers,  [[[disputed]] the region drained by one river
 wear = to retain vitality, to deteriorate
 weather = to withstand (a storm), to wear away
 widdershins = counterclockwise, [[[in the southern hemisphere]] clockwise
 wind up = to start (a watch), to stop (a speech)
 with = alongside, against (as in fighting)
 wraith = ghost of a dead person, apparition of a living person
 x = select (mark with an x), deselect (cross out)
 yuk = to express pleasant surprise (yak), to express unpleasant surprise (yuck)
 zing = to improve (by adding zest, interest or life to), to criticize


A very very short list of contranyms from other languages:

Chinese:
louan = to govern well, to cause a disturbance

Dutch:
ettelijk = many or much, little or few
kooper = buyer, seller

French:
La symetrie (symmetry), L'asymetrie (asymmetry) (homophones)
defendre = to defend, to prohibit
se marrer = to be bored, to enjoy one's self

German:
versehen = to examine, to ignore
Kontrahent = opponent, contractor

Greek:
skhole = leisure, work due to leisure

Hebrew:
hara = to create, to destroy
nigash = approach, draw back

Russian:
slovo = word, secret word or password [[[archaic]]

Sahidic dialect of Coptic:
ehrai = upwards, downwards

Swedish:
maximera = set an upper limit to, make as large as possible
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