Aaah... always the topic of much debate. Once you get down to it and play around with the settings/different emulators/frontends/OS, you will see you need very little to make an adequate, even great emulator PC.
My benchmark tests ran my personal basic setup (Mamewah/XP/pre-0.106 MAME plus most Atari/Sega/Nintendo emulators up to 16-bit) with negligible slowdown/lag as far down as P3 equivalent 600mhz CPU, 128mb ram, on-board graphics and sound and just a 20Gb hard drive. I would recommend though for this kind of setup shooting for at least a 1Ghz CPU with 256mb ram, which will also even run 32X and Mega-CD with no trouble.
For a mid-range system with quicker rom-booting times, no lag and possibility of more demanding, plug-in type emulators, I'd recommend a P4 equivalent 1.6Ghz+ CPU with decent on-board graphics, 256mb ram+, and a bigger hard drive obviously. This can get you decent N64/some MAME .chd/possible PSX emulation and faster response times for MAME rom loading.
I'm currently using a custom version MAME v0.105, Laserdisc, PSX plus all mentioned above with no slowdown or glitches on an ex-business P4 2.4Ghz small form factor PC I picked up for 50 quid. Had to get a 160Gb hard drive to manage the bigger PSX isos and laserdisc games, but that wasn't much so I've got an excellent arcade PC done for £80.
I have spent years testing different emu's, settings, OS tweaks and perfecting the Turnarcades/Mamewah frontend though so I had already ironed out most creases my the time I got round to building my new arcade this month!