I'm probably odder than Unknown_K, I collect white box PC's, often to hop them up with expansions that could possibly put the benchmarks out of their class.
Most sought after item for me would have to be various old pre-1992 white box clones made by GEM Electronic Products in Norcross Georgia. For some reason these people apparently LOVED full size AT cases (as do I, as well as XT clone chassis), enough that so far I've had a 386 DX and a 286/10 come across my path stuck in cases modeled after the Compaq Deskpro 386 and after the IBM PC AT. They also seemed to use the most un-killable motherboards I've ever seen, from that 386 DX thing with SIP memory that was originally in my main computer (which sat in a static filled environment with smoking abound for 6 months before I began to use it again in another computer), to that 286/10 that I got off E-bay for $10 bux which blew a capacitor on the motherboard on the first day, rebooted itself, and kept on going without a single problem since I bought it. Apparently they are one of the less popular whitebox manufacturers, but they seem to straddle the fine line between professional and store bought white-box.
I'm also partial to wacky old ISA peripherals myself, my 486 has quite a few of them under the hood including an old Packard Bell T.V. Tuner Card, and old Reveal FM Radio tuner card. So it doubles as my graphical adventure/old Ultima RPG machine, virtual BASIC programming machine, as well as my television. Who needs an emulator when you can get the real thing, I just hook up my Atari 2600 to the 486 and off I go.
Maybe this stuff does not appeal to many of the people on this site, but then that just means more white boxen for me (as well as a few name brand models, mostly being old Deskpros and Tandy 1000's, and the original PC and XT). Possibly the only computer I'd ever put on display just to say I have it would be an original IBM PC 5150 with original documentation in it's original configuration, and even then, I probably copy all the media so I could use it with the computer to show it off.