It shouldn't have much trouble maxing out older direct-x 9 titles, but it will not max out newer direct-x 11 games. I would expect all games to be playable, but if you could afford to step up to a 7850 1GB, you'd get a lot more performance for not a lot of extra money.
Gotta love this kind of question. There is no such thing as a card that plays "all games at max settings", specially if you consider the custom driver settings (which you should use whenever you have the horsepower as they can improve image quality significantly).
The 7770 is a decent card and can play pretty much any game up to date at decent settings. If you are the kind of guy that wants top notch image quality, buy a top notch card, which the 7770 is NOT.
I'm guessing, though, you do not have the money for that, otherwise you wouldn't be asking about a mid range card. If that is the case, buy the best you can afford.