These days those definitions have gone out of fashion. The internet has lead to a number of fads. One internet meme
rises and another falls and it soon falls so that another can take its place. All your base
fell to The Star Wars Kid
to World of Warcraft
to whatever might come next
FTW these days stands, not for Fuck the World but for the phrase born out of the Engrish meme, IMspeak and drunken internet use. The phrase in question is "For teh win," which so far has gone nodeless. The phrase is used to show support for some idea generally or group. For example:
Anarcho-communism FOR TEH WIN!
Robot Overlords FTW!!
For the typo-savvy out the I am not misspelling 'the,' 'teh' is a common misspelling of 'the' which has come into common, intentional usage for a vague sense of irony on the part of the user. This specifically came out of the IMspeak meme, were people trying to be superior to IMspeakers began using the misspelling as a way of mocking them. Then those who thought themselves superior to those groups mocking the IMspeakers began mocking them with the word. Now 'teh' is simply a byword of meta-internet tongue-in-cheekiness.
According to RoguePoet: The original phrase 'for the win' is a reference to Hollywood Squares. Gary Colman, For TEH WIN!