My system isn't cutting edge but it isn't old; 3gb RAM, 3.16ghz Core 2 Dual, Radeon HD 4800.
Within about four seconds of playing Minecraft, my system will just shut down without warning. It is very upsetting. And only Minecraft that does it; no problem playing the latest games.etc, but Blocky-minecraft causes this.
I can play it on my Macbook Pro, but I find myself not playing it as much as I'd like because I need to clear my desk (a small old writing bureau :$) of keyboard, mixer, junk.etc so I can play it with a mouse.etc.
It's quite intensive yeah, being java. It should hit the cpu harder than the gfx card though, I think. Actually there's a stats thing in game if you hold down... one of the F keys. Forget which. Try that and see if the loads look unusual.