How well will this build be able to handle these games?

That's a perfectly respectable mid-range gaming build. If you can afford it, bump up the graphic card to a 660 or 660 Ti (or get a 7850 or 7870 by ATI, better bang for the buck).

Additionally the AM3+ socket should provide you with a decent upgrade path (to at least the current FX line, or most likely, at least another upgrade cycle from AMD).

Both CPU and motherboard are old models, outdated.

It should run most games on medium settings with good fps, some even on high.

Even an Intel Core i3-3220 with a new Z77 chipset motherboard would be better for gaming.

You don't need 4 cores in gaming, you need more power and speed per core. Most games only use one or two cores.

For $47 get G.Skill Ripjaws X Series DDR3 1600Mhz RAM, much better for gaming:

http://www.newegg.com/Product/Product.aspx?Item=N8...

good build for the money http://www.anandtech.com/bench/Product/680?vs=660 look the blue that a gtx 650ti so expect good fps playing demanding games like bf3 and skyrim get better ram from crucial gskill corsiar good ram is good but other than that its nice it look to be around a $500 gaming pc

the phenom 2 is still better than all fx near it as its a true quad core not a dual core with 4 threads and bf3 is recomended to be played on a quad core which you have and you have a good graphics card so don't listen to the haters.

Very good setup for price,its quite similar to mine.some upgrades you could buy are a Intel i5 CPU,a small ssd and some ram (16gb)

its a good build for games but i would go with an asus or gigabyte motherboard. but thats up to you