I've had a nice, stable Celeron system running for more than 2 years now. A Celeron 333 @ 416 on an Asus P2B, it's acutally more stable when oc'ed than when it's not.
My school on the other hand uses Intel machines and they're very unstable, and you cannot install your own programs on them so that's not the fault. I don't think it's the cpu's fault though, more likely cheap mobos and / or bad setup (cannot prove it as I'll get in serious problems if I, ahem, *aquire* Admin rights to check).
I have had 4 very stable Athlons systems myself: an orginal slot A 700Mhz on a Asus K7V board, the only problem that it had were all mobo related it turned out (wouldn't run with newer drivers for my Asus V6600 Deluxe gfx-card, but the card will use all driver-versions on my old P2B).
My second Athlon rig was a 1.2Ghz T-Bird on a MSI K7T Turbo LE, was stable until the mobo died.
The third system was a 1.4Ghz T-Bird on a MSI K7T Turbo Raid, also very stable. It's was nearly impossible to make it crash.
And my current XP1600+ on a MSI K7T Pro2 RU is stable, I've newer had it crash unless I oc'ed too much.
'nuff said, AMD is just as stable as Intel. All the Athlon rigs I've had has used Via-chipsets which should be notoriously unstable, and yet I've had no problems.
Oh yeah, the mobo has just as much to do with stability as the cpu, probably even more.