Admittedly, most of what I have isn't particularly rare, just uncommon. But I do have a few bits that might make the cut.
1) A 1969 Micro-Switch Keyboard. I have no idea what it came from, as I was never able to identify the board. But it feels really nice to type on. Maybe I'll figure something to hook it up to someday.
2) An Alspa ACI-2. Currently sitting in pieces, but near as I can tell, I have all of them. A the moment the PSU is with a friend who's trying to reverse engineer how to fix it.
3) An iCot ICOBUS 757-14 Terminal. I know next to nothing about it (other than it works).
4) An original Quadlink Apple II ISA Card. All I have is the card, so I haven't been able to test it. But I did stick it into my 5150 and it didn't short out or anything, so that's a good sign. Eventually I'll be sticking it into my 5160, but I haven't gotten around to it yet. Also, I need to find the software.
5) An original Apple IIe card with the original unobtainium Y Cable! Not sure how rare the actual card is, but that cable... seems to be near impossible to find now-a-days. Currently it's installed in my Macintosh LC III. Works perfectly, and yes, I have the software for it.
Not sure if they're particularly rare, but others listed them... so:
6) A Macintosh IIfx. Missing it's hard-drive, but it works all the same.
7) An Apple ][ Rev 4 board. It's fully functional, and had been using it as an "original" Apple ][, but I swapped it for a Rev 2 board. Unfortunately, I still have a ][+ sticker and serial number on the bottom.
And just to round it out... Not rare, but uncommon:
8) A Commodore VIC-20 with original PET-style keyboard. Works perfectly and is my preferred VIC.
9) An Amiga 500 with "Chicken-lips" keyboard.
10 A TRS-80 Model III with original high-res graphics board installed.