Hey Steve,
Well, it's a tough question as it's often a matter of hunch. Well, it all comes down to what kind of sites you're running...
If they're for your aunt running simple guestbooks, then an old 200mhz with 64 megs of ram would be enough. And if it's largerscale datawarehouse solutions, then dual 733MHz Pentium3 with 512MB ram would be adequate.
So, you see. There is no general rule of thumb to what kind of hardware needed. But better buy it too big than too small, ehh ? My experience tells me to focus on the amount of ram rather than processor. running several apache and IIS based servers it shows RAM is what is needed.
I would stick to Pentium2 / 3 for reliable and fast hosting, but a Celeron processor... hmm, I never tried that...