I had an eMachines Celeron 633Mhz with 192MB of RAM and a 32MB GeForce 2MX for a month shy of three years, which I got for Xmas in 2000. That was reasonably capable of playing games when I first got it - I had GTA2, Motocross Madness 2, Hitman, NFS High Stakes and used to play loads and loads of Rogue Spear/Urban Ops. It did start to feel very slow after about a year and a half though. In the final year I had it, my friends and I would have small LAN parties and my machine did start to act up a bit! Homeworld 2 kicked up errors about not meeting system requirements, not having sufficient video memory, not having shaders etc although surprisingly it still allowed me to attempt to play it, albeit with bizarre looking graphics and missing pieces. Suffice to say, I lost that fight.
We also gave MoH:AA a go which actually ran OK, although for some completely unknown reason the main menu music kept going (and looping) even when I was actually playing. Oh, and every time I picked up health or ammo it'd say "Got 10 Got Got" instead of telling me what I'd actually collected. By that point I just found it hilarious.
I used to do everything I could to reduce system overheads with that machine though, by not having a background image and closing anything unnecessary that was running in the background. So nice to not need to bother with that sort of effort these days!