I love that you posted this topic as my brother and I are actually collectors of rare or semi-rare games. Actually, I tend to collect retro games in general and I have a few semi-rare ones myself. But rare games? I don't own many of those, however I did have a loose cart of Bubble Bobble 2 about a month and a half ago in which I bought for just $1(yes, that's right). I periodically make posts on Craigslist to buy games, in which I will collect some but usually resale them. Consoles may not count but I have a NES top loader, Joshua: The Battle of Jericho for the Genesis which is semi-sealed, Digimon World 2, DDR Mario Mix for the Gamecube with the dancepad still in the box; I also have Chrono Trigger with everything for the SNES, Super Mario RPG and many other RPGs for the SNES, Lunar Eternal Blue complete for the ps1, Marvel Vs Capcom 2 and Skies of Arcadia for the Dreamcast. I have a 3DO as well with a few fairly common games such as Myst.
My brother has had a few rare titles too such as Little Samson for the NES, a factory sealed copy of Menace Beach for the NES, and some others(EVO the search for Eden and Mega Man Legends 2) and hes sending me a copy of Mega Man x3 soon which is also quite rare. That's about it as far as semi-rare or rare games go - I can't wait to see what some other people have in their collections.
PS I would love to get my hands on some extremely rare titles such as Stadium Events NTSC, Kizuna Encounter(Euro PAL version) for the Neo Geo, or Birthday Mania for the Atari 2600.