Random conflict
According to Maximum PC, May 2006, Antec Neo HE series PSU + Asus A8N32-SLI or A8N-SLI mobo results in boot failures and random crashing.
Hard drive issues
Large PATA drive + old BIOS
See Curse of the Large PATA Drive. Just don't do it.
Random conflicts
According to Maximum PC, May 2005 and Tom's Hardware Forum, nForce4 mobo + Maxtor DiamondMax 10- or 11-series hard drive results in drive not detected or hang while booting Windows.
2013-05: IBM Deskstar 120GXP model IC35L060AVVA07-0, 60 GB, 7200 RPM, ATA-100: Two different drives of this model caused two different computers to hang during boot. If the BIOS was configured to ignore the drive, booting would proceed normally from other devices, and the drive could then be accessed from Linux with no hint of trouble.
Graphics card issues
Linux driver purges
The first great purge was the release of XFree86 version 4 in 2000, when they made incompatible changes to the driver architecture and nobody had the time or interest to rewrite all of the old drivers. Since then the obsolescence treadmill has only gotten worse. Details moved to X-Regressions dot ARRRGH.
Random conflicts
nVidia RIVA TNT2 64 + 430FX chipset
This combination refused to work and I don't know why. I just got garbage on the screen (colored blocks and noise that shifted and changed). I put the same video card in a different PC with a slightly newer chipset and it worked fine. Different PCI video cards in the same slot on the same PC also worked fine, even a 3dfx Voodoo3 2000 which was from the same year as the TNT2.
http://www.flaterco.com/kb/PC_incompatible.html