Currently, which models of desktop processor from either Intel or AMD offer the best value? I'm building a desktop PC, want more than two cores and am considering spending under $300.

Doesn't have to be cooled passively, although I will at least want a good aftermarket _quiet_ CPU cooler.

It depends on your locale and how you measure value.
With my local prices and considering strictly the CPU, the best general value would be the G530.

The number of cores is irrelevant since different designs do not include the same things in what their vendors call "core" and there are large differences in performance.

You say you want more than two cores. The only viable options in that area is quad-core Sandy Bridge processors. More specifically, core i5 2300 or 2400 if you don't want to overclock. Otherwise, the i5 2500k for overclocking. The 2600k is only for users who need the hyperthreading.

What exactly are your needs for the CPU?

No AMD candidates?

viewtopic.php?f=23&t=63794

AMD has core count, which is irrelevant.

I thought you meant $300 for the whole computer, not the CPU. $300 CPUs are poor value today. It makes little sense to pay more than the cost of a 2500K for a desktop CPU and I personally would not consider paying more than the cost of a 2400. The 2500K is for overclocking and if you want to overclock, it would be best to wait until April for the 22nm 3570K.

I'm looking at newegg's available i5 and i7 LGA 1155 processors. What's the difference between K-series, non-k and S-series processors?

K: unlocked multiplier, i.e. able to overclock.
non-k: not possible to overclock noticeably.
S: power-saving

Below $300, if you apps dont benefit a lot from hyperthreading, i5 2500K imo is a really nice CPU for the money, if you dont need the HD3000 or an overclock CPU, check the i5 2400. Now if you do benefit from hyperthreading and still below $300, Intel Core i7-2600.

All the intel CPU line will be referesh by april 8 with ivy bridge, expect replacement both the i7 2600K and i5 2500K on launch, the gains on performance wont be that big as its mostly a die shrink, maybe around 10%, but they will consume less power, but one decent gain in the integrated GPU, the HD4000 will be around 30% faster than the HD3000.

Depending on the mobo and case, if you dont have any clearance issues i recommend, Thermalright HR-02 Macho or Scythe Mugen 3.

What will be using the PC for? As long as you aren't gaming there is value in the onboard GPU on Sandy Bridge processors as that should be enough graphics power. And it means no discrete graphics card which means less heat and (perhaps) one less fan assuming that you were considering a graphcs card with a fan.

edit - Here is a quote from a SPCR review in March of 2011 - I don't know enough about AMD's lineup to know if things have changed materially in the last ten months:

The HD3000 can even handle some gaming (I was playing SC2 on my 2500K HTPC earlier this evening). Other games, not so much - from what I've seen, Civ5 is essentially unplayable on it. Certainly, for gaming in general you'd be better served going to an i3 and using the savings on a dedicated GPU. I'm just waiting for Kepler.