The closest to rare I have is MGS 1, which tends to go for $30 on ebay, as opposed to say, Tekken which is only 10. (Then agian, MGS has two disks, so that could be a factor for the price)
Aside from that the games I have are either digital or easy to come by.
Probably the only one I can think of is Mr. Moskeeto (PS2). It sold poorly in western regions and arguably isn’t a common sight. You’re a literal mosquito and suck blood from a family to prepare for winter.
Oh Japan…
Edit:
Another one I remembered: War of the Monsters (PS2).
It wasn’t particularly successful similarly to the former, but nonetheless a fun movie monster parody fighting game.
It’s actually been remastered for PS4. I can recommend giving it a spin.