I have probably said this before somewhere but I really love
Cleopatra Fortune and wish more people knew it existed. It's a pretty fun falling blocks puzzle game that does things a tad different than most of the usual ones that come to mind (though not as different as, say, puyo puyo.) I think it was released on the saturn and PS1 and you can find those for cheap (PS1 anyway, it's seriously like two dollars after shipping on amazon if I recall) or get the Taito Legends 2 collection for the PS2 or Xbox (which shouldn't cost too much but comes with 40 other titles as well, and it's the actual arcade version and not a port.)
Speaking of the Taito Legends 2 collection
Elevator Action Returns is really fun. Three characters to play as with their own strengths and weaknesses, lots of nice weapons, it's worth a look. One last thing from there since I'm thinking of it is
Puchi Carat which is sorta like Breakout.
Getting away from that collection (which again, has 40 some odd extra titles on it, I'd definitely pick it up if you can) there's
Sequence, which is half rhythm and half RPG, if I had to describe it. The gameplay's great, with separate DDR/Stepmania-esque screens for attacks, defense and mana collection. My only real gripe is that there's a rather limited number of songs (though it's not too limited to be a huge problem, as far as i'm concerned anyway.)
Arcana Heart 3, which I believe was done by Arc System Works, is a pretty cool fighting game, though the all-female cast may put some people off I guess. I liked the their Arcana system, which was kinda similar to stands/persona in a way. Only you could pick which one you wanted for your character instead of having a set one, and it was mostly just bonuses to their skill rather than being an assist-type.
I don't know how "unknown" this game is but
War of the Monsters was my first PS2 game and to this day I love it. The world needs more fighting games with giant monsters and environments as destructible as this. Another game I'm not sure if I'd call a rarity but I'll just assume it is would be
Z.H.P. Unlosing Ranger vs Darkdeath Evilman. Great dungeon crawler type game for the PSP (and Vita, on PSN) by the same guys who did Disgaea. Definitely worth picking up if you enjoy the genre or toku shows in general.
I'm sure there's more somewhat obscure games that I've played and loved but those are the only ones that come to mind at the moment.