Desktop hardware that doesn't work with Linux...hmm...
Well, ATi cards have downright awful support. Fglrx was a lame attempt at first, barely pushing decent FPS in games, and it didn't support AIGLX. Now, they've worked harder and implemented AIGLX and made it better, but it's still not in the Ubuntu repository and even after using the .bin file ATi provides, it doesn't work quite as well as the Windows Catalyst drivers.
nVidia works great, at least my old MX420 works fine even with Compiz Fusion.
However, desktop surround sound (Realtek integrated audio) doesn't work, though stereo does.
The biggest issue is desktop wireless cards. I don't own one myself, but I tried installing Ubuntu on my friend's computer (he saw my Compiz desktop and wanted it for his PC). The LiveCD wouldn't boot GNOME because it was stuck complaining that it couldn't find Broadcom firmware. For some reason, my laptop's wireless PCMCIA card is Broadcom and it works just fine with the Restricted Drivers Manager (I'm using the card right now in Ubuntu), but my friend's desktop PCI wireless card stopped Ubuntu from even starting up.
Actually, even my laptop is pretty well supported...The only thing that doesn't work is the Rage Mobility M3's integrated TV-in chip (Philips PhilDec Capture) [the Rage graphics chip works fine, the capture card doesn't]. Also, the ThinkPad buttons don't work right, but they used to. Ubuntu's new hotkey-setup package broke them when 7.10 came out.
Ubuntu also works fine with the integrated graphics chip in my desktop that I didn't even know existed until recently...I needed to take the motherboard out of my Pavilion, and on the back was this thing that said "Do Not Remove" screwed into the board...so I removed it, and behind it was a VGA port. I plugged my monitor into it without my AGP card in, and it worked fine (S3 Savage I think, didn't have very good 3d performance). Wonder why HP covered it up...even if the AGP card did disable it,...stupid PC manufacturers.