I personally am using right now the AMD 1045t x6, I have it overclocked to 3.8Ghz and with turbo I got it to 4.5Ghz. Note the turbo speeds are on liquid cooling now, but previously I had 3.8Ghz pretty stable using the Coolermaster Hyper 212 Evo, a budget $25 cooler. This chip you can get for about $60-80 bucks, 6MB of cash, overclocks great, and it's a real trooper for overclocking, I mean I've put it through hell and it's still alive. It's been running long since last June or so.
I plan on upgrading to the 8350 but I love this chip, I'm considering framing it on the wall because iI broke the third superpi record for this chip next to someone using liquid nitrogen.
ANYWAY yea this chip is great in the AMD line, it's actually like an upgraded 955 black edition with six cores. Just remember to overclock it, stock it's a slightly weak 2.7Ghz.
I think it's the best "budget" AMD you can get, it's very good. I am mainly recommending it because it's done producing recently so alot of stores are clearing their stock of them at dirt cheap prices. If not the 1045t, I would hugely recommend an Intel i3 like everyone mentioned above. I've seen the i3 do amazing things including 5Ghz overclocks! That CPU runs for a very cheap, Newegg is actually having a $10 sale on this one right now ( I think it ends very soon):
I almost want to build a budget intel system with that CPU, it just looks fun to play with and the price is attractive. The only thing is the cache side is kind of low. Other than that, fast speed, lower heat/power consumption.