Core2Duo E8400 or Xeon E3110 or Core2Quad Q8200/Q8300 or Pentium E5200

Scratch off the pentium... it's useless.
Xeon's probably not going to be very good value compared to the others...
Many games these days don't fully utilise dual-core machines, never mind quad cores. With that said, the E8400 is probably the best of what you've listed.

That said, the AMD Phenom II x3 chips are the best bang for buck chip for pretty much everything lately.

Well from the list, the best value would be obviously the E5200 once it is overclocked...
Next in line the E8400...

Well Yes generally the E8400 is the best but think a $70 CPU can overclock more than 3.4GHz easy and when its performance is compared with a $170 E8400, would give the E8400 a run for its money...This is only the case if the games are more of a graphics card dependent than the CPU dependent...
But in games like GTA4 or FSX, which are CPU as well as GPU dependent, the E8400 will shine...

The Core2Q are not good for gaming...YOu can get them if you want a overall performance improvement...But specifically for games, it wont be better than the E8400...

This is a very interesting discussion. Of course an E5200 running at stock speeds cannot compete well against the E8400. But seeing as that the E5200 is suppose to be able to overclock from 3.7 to 4.0 GHZ it can give the E8400, running at stock speeds, some stiff competition. Of course the E8400 is also suppose to be able to overclock to 3.6 to 4.0GHZ.

But we must remember that today's games are more dependent on gpu power. I have come across many boards that say that it's better to go all out and get the best available graphics card one can afford and pair it with a "low level" or mid range cpu. Now if a person's main task to to build a computer that can do alot of things well besides play games on a budget then obviously the E5200's low cache will not be the solution. But for the purpose of overclocking and gaming on a budget then the E5200 is the way to go.

I am also in a similar situation, but my two choices are the E5200/E5300 or the E7400. I'm waiting for the C2Q's to drop to my price range.