I realize nobody has probably done a thread about this yet! So, now is a better time than any, since it being late and all the rarity of rare games has probably sore by now. I will start off with my two Saturn games, only rarities I actually own.
* Street Fighter Zero 3 * The infamous, definitive SEGA version of Street Fighter Alpha 3, which I can vouch is pretty dang good. Definitely the gem in my collection for being the most expensive game I own. Has everything too, so I have a pretty solid copy.
* Akumajo Dracula X: Nocturne in the Moonlight * Finally hit the triple number zone recently, so somewhat rare now. Aside from rarity, it is known for being a horrible port of the PSX classic. Personally, I wish this was the game given more effort since it deserved it. I could have lived with dithering effects if they did them better and slowdowns were, and SHOULD have been all absent since the Saturn is a 2D Beast. But, I still like playing it since it has so much more stuff to do and items to collect and Maria to kick ass with.
some are more rare/available than others, but i'll go by console, and all are loose copies unless otherwise noted:
nes: bucky o-hare, metal storm (have a handful that go for a lot now, but not sure on rarity, as with the ones i've listed - i think they're more in demand than "rare")
snes: ninja warriors, castlevania: dracula x, e.v.o. the search for eden, demon's crest, hagane (sfc japan version), ninja gaiden trilogy, earthbound, chrono trigger, metal warriors.
genesis (all have at least hard case/artwork): alisia dragoon, el viento, cadash, chiki chiki boys, high seas havoc, mega man: the wily wars, alien soldier, golden axe III, skeleton krew, splatterhouse 2 and 3, the punisher, valis and valid III, zero the kamikaze squirrel
saturn: akumajo dracula x gekka no yaso kyoku (castlevania sotn) guardian heroes primal rage (pal)
i have more newer systems/games but this took a while!