My unfinished computers:
Compaq Deskpro 4000N: My family's first computer, way back when I was in highschool: Pentium 233MMX, 32mb ram, .....parted it out and never finished putting it back together. Needs a new mobo battery, an optical drive, floppy drive, etc. Basically too old, but hey, it's the first computer, so there's nostalgia value. It's been about 2 years since it last ran.
Foxconn E-bot: My silent mini PC project. Still need to passively cool powersupply. Been 9 months, but I'm making progress.
Dell Dimension XPS r450: Needs DVD drive and software, and probably more ram. I've had it for a few months now.