CToleR :
Would this system handle today's and near future most demanding games like Crysis 3, Battlefield 4, GTA V, and others at 720p resolution on high or medium with good fps?
CPU: AMD FX-6300
GPU: HD 7770
RAM: 8 GB DDR3
Windows 7 64 bit
Eff that. It runs most games at "high" in 1080p.
However, you might have to tune it down to about "mid/low" for the absolutely most demanding games in 1080p.
If you're only using a 720p monitor, then you can probably whack everything up to ultra and be just fine
EDIT: You shouldn't have to worrying about CPU bottlenecking either. With perhaps a modest overclock, the FX-6300 is powerful enough that it certainly won't bottleneck the HD 7770.