Building a gaming pc around 500$

^ Both the CPU and GPU are very good options for gaming...you can also take a look at the Athlon II X4 Quad core CPUs...they will perform very similar in gaming and better in multitasking...
As for the mobo
GIGABYTE GA-MA770T-UD3P
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
http://www.newegg.com/Product/ComboDealDetails.aspx?Ite...

RAM
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

HDD - Samsung F3
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

CASE + PSU
Antec Sonata III + 500W EA
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

ok, thanks  but the amd processor is a good choice? i shouldnt go with an intel processor? ive been getting that advice from some people, although im not sure how knowledgeable they really are..

Really, its all personal preference concerning CPU's. All benchmarks have pretty much the CPU's in the same price range performing very similarly. Most of the time the difference is so negligible outside of benchmark testing you wont ever see the difference. But general price for Performance wise AMD is the best choice, usually being quite cheaper then intel for similar performance. Especially if your willing to overclock at all.

alright! good then, thank you. The graphic card is a XFX RADEON HD4870 1GB GDDR5 PCI-E DVI for around 110 dollars, is that a good choice?

^ Oh yes that is a good choice and a very good deal as most of the HD 4870s hover around the $150 price range...

In the $500 range, AMD is pretty much your only choice.
The case+PSU combo that gkay09 linked is the rare exception that proves the rule that PSUs that come with a case are crap. The 500W Antec Earthwatts in that case is excellent. The case itself is one of the most solid cases I've used in the last decade, and harkens back to the day when even cheap cases were heavy.
The only concern with that case is that it sacrifices cooling for quiet. If the HD4870 you're getting exhausts its heat, you should be fine. Otherwise, you may wish to consider a better-cooling alternative.

thank you so much for your input 

Alright, just ordered the parts  in the end i made a few changes and went over the 500, but i think i will be happy in the end 

AMD Phenom II X4 955 Black Edition 3,2GHz Socket AM3 Box
Gigabyte GA-MA770T-UD3P, Socket-AM3
PowerColor Radeon HD4890 PCS+ 1GB
Corsair 4GB (2x2048MB) 1600MHz XMS3
Cooler Master Elite 333 Black
Corsair VX 550W PSU
Sony Optiarc Intern SATA DVD±RW 24x AD-7240S