The rarest pieces that I own (as far as I know, and off the top of my head) are:
E.A.S.E. Magnum Opus One Line Stage (only 50 were ever made).
Esotec SD-4000 cassette deck. (The Esotec branding makes this very rare; as a Marantz-branded unit, it is not so rare. I've only ever seen ONE other Esotec one, in an online listing on Japan Yahoo a couple years ago.)
The "Dragon" receiver. a classic silver-faced monster receiver that vaguely resembles a rebadged Pioneer, but doesn't exactly match any receiver that I've been able to find. I haven't found any evidence of another one in existence. (And no, it is NOT a Nakamichi!

) I suspect it might have been made in Taiwan, but that is pure speculation based on some apparently Taiwan-made internal components.
Harmon Kardon "Citation The Receiver". I believe two other AKers have these, but they make up about half of the total owners I've ever found online; these receivers were sold in small numbers, and apparently are very rare. My "Emerson" rebadge of the 930 receiver is rare as a rebadge, but the basic unit under the original H/K brand isn't so rare. I also have an early H/K "Stereo Fiesta" receiver, which has the distinction of being the first stereo receiver ever commercially sold.
Musical Fidelity MVX-2 preamp, with separate power supply. A Tim de Paravicini design from the earliest days of the brand (it was originally sold under the "British Fidelity" moniker), seldom seen on the market. I've seen at least two others online (one in an eBay auction).
The Pioneer Pl-L1 linear-tracking turntable. Considered "XXX-rare" or "ultra-ultra rare", but a diligent and patient searcher could get one from Japan. I know five of these were originally imported/sold here, and there are at least three still in Hong Kong (probably a few more?), but I don't know of any other AKers who own one.
Peerless speakers. These are early (50s? 60s?) vintage, and definitely appear to be factory-made, NOT kits, which makes them very unusual. While Peerless drivers and kit speakers are fairly common, I've never seen another pair exactly like these, neither in real life nor online.
I have some others that are not exactly commonplace (eg, SX-1980, PL-C590, H/K Citation 11 and 12 deluxe, GT-2000 --the latter rare only outside of Japan) but which I know at least several other Akers have, so they aren't all that rare --esp. on AK-- either. I might be forgetting one or two other obscure rarities of lesser note.
Oh, do Boomboxes count? I have several of the very rarest models on the planet, ones that even most hard-core collectors don't have.
Future rarities:
The two other rarities that are "on the horizon" for me to bring home soon are the Yamaha 101M and the Sequerra Signature Series speakers, both of which I've talked about in previous threads. While a few other AKers have the commercial equivalent of the 101M, and local AKer Sundog used to have one, I think I might be the only active AKer to have a 101M. The Sequerra Signature Speaker is vaguely similar to some other AKer-owned Sequerra Pyramid spealers, but not the same. There were probably only a couple dozen of that model made in total, and there might be fewer than 20 on the planet today, so I wouldn't expect anyone else to have those same speakers, except by extreme coincidence.