One of my first HL1 installations (way back when) was on a P2 with a 32mb graphics card and 128mb of RAM.
HL1 will run on just about anything. However, I have noticed some graphics issues using HL1 on newer machines. My 6800GT had to be tweaked to run HL1 correctly, as it kept trying to making all HL1 games way too dark and oversampled the textures. So I guess I can say that the only problems are having TOO MUCH of a machine, rather than too little.