The i7-920 is still an excellent CPU, IMO it's one of the best Intel has made in the last few years. I can play BF3 on my PC maxed out no problems. You could look into getting a nice CPU cooler like the Noctua D14 and try overclocking your CPU to 3.2, maybe 3.5GHz.
I'd check the dimensions of your case before buying a huge CPU cooler like that, but maybe a new case like the Corsair Carbide or Cooler Master HAF 932 wouldn't be a bad thing, either.
Definitely upgrade your graphics card, maybe increase your RAM to 3 x 4GB instead of 3 x 2GB (your motherboard should be capable of this - check with Gigabyte just to make sure), but that's about all you need.
For video cards, I'd suggest either an EVGA GTX 570 (which comes with free Batman: Arkham City), or maybe a Sapphire Radeon Flex 6950, both are pretty excellent and comparable cards.
And at some point look at adding an SSD in the future and using your primary HD as your secondary, that will show massive improvements in load times with resource hungry games like BF3.