I have some arcade stuff that could probably be considered rare depending on the criteria. I have a US Solomon's Key PCB, which I have never seen for sale anywhere in the 10 years I've owned it, and believe me I've been looking! I'm the one who dumped the ROMs, even. It's kinda funny actually, the Tecmo Classic Arcade compilation for Xbox uses the Japanese ROMs and came out before I did the dump -- I'm guessing that even Tecmo themselves didn't have the code for the US version around anymore. I'm not even sure if it got a proper US arcade release, or if it was just some sort of prototype situation. The Japanese PCBs are more common but still only come up a couple times a year on Yahoo and sell for $6-700. (In case you're wondering, there's really no difference other than the title screen, which is actually uglier in the US version!
Some other semi-rare PCBs I own include games like Libble Rabble, Outfoxies, Cowbows of Moo Mesa, Technic Beat, Eco Fighters (US/Blue.. used to sell for a mint until people MAME'd it and realized they didn't really like it that much!), Megaman the Power Battle, Tenkomori Shooting, etc. Like most things listed in this thread, none of these are super-duper rare, but they'd require some pretty annoying amounts of searching and money to track down. Unlike stuff like Panzer Dragoon Saga, which is on eBay 24/7/365 if you happen to want to pony up the cash for it.
I've owned a lot of rare dedicated cabinets as well, but in recent years I've been trying to concentrate more on games I actually like to play. Having something the size of a fridge sitting there just because it's "rare" gets old when you realize you never really want to play it (see: Williams Turkey Shoot), and the same goes for owning games in inferior/weird formats just because of their rarity (Joust/Tempest cocktails, etc). I do own a Pop'n Music 14 (Fever), though, which could be considered rare in the US -- I think there are 10 cabinets in the entire US, last I checked. And about a million in Japan. But hey, try getting one shipped over here. It's not fun!
Last year I found a stash of very old arcade games that included the second-known-to-exist game "Hi-Way" by Atari, and the only-known-to-exist (really) "Pursuit," also by Atari, which had only been seen in promotional flyers beforehand. I passed them along to a friend of mine who runs
an arcade museum and aspires to own (and include in the exhibit) every Atari game. If it ever comes your way be sure to check it out, he has some really awesome pieces in the lineup.
