I have 4 standards of completion for games:
BEATEN: I have seen AN ending, other than a non-standard game over. Basically, I've got to the first possible point where I can claim I "beat" the game. In a game with multiple scenarios (like a multi-faction RTS or a fighting game) this will be the first time I beat it with any single faction/fighter. In Guitar Hero III terms, this is beating Lou on Normal difficulty.
COMPLETED: I have seen the TRUE ending or all major endings. In games with multiple endings I have got the best ending, as long as it isn't an absurdly difficult "secret" ending. In game with multiple scenarios, I have beaten all the major ones- I have won all faction campaigns and beaten the game with every character. This is the point where I consider the game to be "won" and can safely put it away/uninstall it without it continuing to niggle away at the back of my mind. In Guitar Hero III terms, this is beating Lou on Expert difficulty.
TWINKED: I have dug out every secret and seen everything the game has to offer. This is very difficult and often requires multiple playthroughs. I have seen pretty much everything, beaten all secret bosses, found every bonus item and own the top scores list. In Guitar Hero III terms, this is Completed PLUS beating every song (including 'Through the Fire and the Flames') on Expert difficulty.
UBER-TWINKED: This is the ultimate level, only for tiresome obsessives. I have done EVERY SINGLE THING IT IS POSSIBLE TO DO IN THE GAME. There is not ONE drop of playability left in the game. I have found every single item in the game in a single run, no matter how trivial. My character has not only had their level and stats maxed out, they have been optimized to be ultimately powerful, even though they could wipe out the entire game 30 levels back. I have beaten the entire game without taking a single hit, with all possible self-imposed challenges (like low-level runs, speedruns, no equipment runs etc) In Guitar Hero III terms, this is 5-starring and 100% completing every single song in the game, using star power to get the absolute highest scores physically possible for each and every one. I never do this, but it has been done.
As I said, my standard of "winning" a game is the 'Completed' level. Basically, when I've seen everything worthwhile that doesn't take an absurd amount of effort.