I think I would like a couple of different rigs for playing old games, depending on how new the games are:
For really old games I'd like:
CPU: something between a 386DX-33 and a 486DX4-120. Most of the games made for 286s and lower would run fine using slowdown utilities or other hacks.
RAM: somewhere around 16MB would be fine.
Video: a 512KB ISA SVGA card at minimum, 2MB PCI/VLB at maximum (with VESA 2.x support)
Storage: probably somewhere between 512MB and 1GB would be fine because the CD-ROM games back then didn't need to use much hard drive space. A 4x or higher CD-ROM drive would be good too, along with 5.25" and 3.5" high-density floppy drives.
Sound: i have lots of old sound cards, so I might put in a SB16 or an AWE64 Gold. I could even use one of my SB16's as a controller for a CD-ROM drive I think (I don't know how good the IDE controller on those is though because I've never tried to use them)
OS: DOS 6.2x and maybe Windows 3.1 or 3.11 for the few Windows games that existed back then.
Other: A nice old 15" monitor should suffice, since old DOS games didn't use anything higher than 640x480. 320x200 graphics look super-blocky on 17" and larger monitors 😉 Serial or PS/2 mouse (2+ buttons) and AT or PS/2 keyboard.
For newer old games I'd like:
CPU: something between a P133 and a P266. A bit lower might work but I wouldn't want to go higher because games like Daggerfall can't deal too well with it even with slowdown utilities.
RAM: 32MB should be about right. 64 at maximum.
Video: 1MB PCI at the very least, but a 2MB or better card would be nice (they're cheap anyways). It may even be fun to throw in a 3dfx Voodoo2 for the DOS Glide games I missed out on.
Storage: 1GB at the very least because I'll almost certainly want to do full installs of one or more CD-ROM games. Maybe an old 6GB drive would do nicely. A 16x or higher CD-ROM drive would be good too, as well as a 3.5" floppy drive.
Sound: Same as the other computer. I might consider putting in a PCI card (like an SB PCI128 or SB Live! Value) if it doesn't give me too much trouble (that way I could play Win9x DirectX games and MP3s)
OS: Win9x (95 OSR2, or 98SE probably) on a FAT32 partition, and maybe a dual- or floppy-booted DOS 6.2x with a FAT16 partition in case some games or hardware can't deal with DOS 7 or FAT32.
Other: At least a 15" monitor...Might want to be able to do 800x600 or even 1024x768 in a few games and in Windows. PS/2 mouse (2+ buttons) and keyboard.
Other toys I'd like to have: A Roland MT-32 synth module, a Gravis Ultrasound (GUS) ISA card, and one of those ISA Roland Sound Canvas-like cards (or maybe an external Sound Canvas synth module). Some fancy joysticks might be fun, although I've never been too much into flight simluators (except for stuff like the X-Wing series). Connecting everything via a LAN would be handy too (although getting a DOS box, a Win9x box, a WinXP box, and who knows what else to talk to each other would probably be quite a challenege on the software side). Oh, a Dolby Pro Logic decoder would be fun to play with too because a lot of the video sequences in games are recorded in Dolby Surround (I had a cheap Radio Shack surround decoder once and the opening movies for the Baldur's Gate games and Icewind Dale sounded mega-cool with that third sound channel in the rear)