I'd say AMD/Intel.
The palm one isn't that big, and the voodoo one is over.
ATI vs Nvidia is big, but not everyone is into gaming, so that's a smaller scale war.
The mac vs windows one is second I'd say, but it seems pointless.
If you're a mac user, you're a mac user. If you're a windows user, you're a windows user. Granted, there are some people who do use both, but they're mostly one way and the other only on occasion. Also, there seems to be relatively little jumping going on. eg, Jim buys a mac, then buys a PC, then goes back to a mac...
AMD/Intel is bigger IMO because the cpu speed war makes consumers feel like they have a slow computer after 6 months. Once that old computer is "slow" the person goes back into the market for a new processor. Switching between AMD and Intel is very easy to do (can you tell whether you're running an AMD machine or an intel machine without looking it up in the device manager etc?). Most people will go for a price/performance sweet spot, and the war is on to market a chip right in that spot.
I game, but not much, as I still have a GF2. I've been a PC user since the first one my family got, and am not likely to switch. I HAVE, however had systems with amd chips, and systems with intel chips, and bought whichever one offered me the most bang for the buck.