Ok. Your CPU is a dual core without hyperthreading, so the very latest and most CPU intensive games will probably not run very great on it, but if you don't play games with very fast paced action where you want 60fps, you can probably get pretty far with a new video card for as little as 100 bucks. Settling for 720p will open up for quite a few more games too.
With a 100 bucks video card upgrade, I expect that you will be able to play for example FO New Vegas, Portal 2, Mass effect, and Skyrim at least better than PS3 or Xb360 can do, but you probably won't see the same level of image quality as you would get on a PS4. Not for all games at least. It will vary a bit.
It'll most likely play many PC-centric games like DOTA2, LoL, Civilization 5 and Starcraft 2 without a hitch as well.
Your CPU will probably show its limitations in games with lots of NPCs or other movable objects first. In some games, like Skyrim, you can decrease the amount of on-screen characters and objects, and that would probably help.
You should probably try to go for a video card that doesn't use an enormous amount of power, unless you know you have a decent PSU in that machine.
Something like a GTX 750Ti should be pretty well matched in performance compared to the rest of your parts, and doesn't use a lot of power. It's not hard to install, but make sure you have enough space for it before buying, if you decide you want one.
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