A 1.5-gigahertz Intel Pentium 4 chip or AMD Athlon 1500.  384 megabytes of memory.
Two gigabytes of hard drive space.
An nVidia GeForce 3 graphics card or better; or an ATI Technologies 8500 or better.
If your existing rig doesn't meet these specs, here's a guide to beefing it up to play Doom 3 in all its gory glory.