Whether they be valuable/collectible, just hard to come by, or just games that most people haven't heard of, which are the rarest in your collection.

I pretty much never sell my games and systems any more (I used to as a kid, unfortunately, and got rid of some really good stuff for NES especially ), but some of my rarest and most obscure stuff is...

- A DS Download Station cartridge (Vol. 3)
- Game & Watch Collection 2 (Club Nintendo exclusive, unopened)
- Electroplankton (DS)
- Shikakui Atama wo Maruku Suru: DS Kanji no Shou (obscure kanji learning game for Japanese kids)
- Cubivore (GC)
- 2 different GameCube demo kiosk discs

I also have a couple Japan-only games, but they aren't really anything special since anyone can get them fairly cheaply on ebay. And I have a couple unexpectedly valuable games like Pokemon HeartGold and Fire Emblem: Path or Radiance.

If you are talking about just games, then I guess my Arcade Compilation game for XBOX 360 is considered rare since they are hard to come by. I also have a Jumper Pak for N64. 

I don't have it anymore, but probably the most obscure game I've had is Dark Angel: Vampire Apocalypse for PS2. It was basically an unfinished Diablo clone that, all in all, was actually pretty damn terrible. It's tied with X-Kaliber 2097, methinks, in terms of obscurity, but at least the latter was relatively enjoyable, especially the soundtrack. That's what got me into Psykosonik, and what I believe to be their best song.

While I don't have any games that are super rare, I do have a few hard to find and somewhat expensive to buy games around.  For the Sega Genesis I have Master of Monsters and Herzog Zwei.  For the Sega Master System I have Phantasy Star 1.  For the IBM PC I have Leisure Suit Larry 3 (3.5" floppy), Superhero League of Hoboken (3.5") Pools of Radiance (3.5"), Curse of the Azure Bonds (3.5"), DragonLance Limited Collector's Edition with Champions of Krynn, Death Knights of Krynn & The Dark Queen of Krynn (3.5").  I also have Nobunaga's Ambition II on 5.25" floppy that is in new condition. 

I also have the consoles and computers to play these games.  I obtained an IBM 5150 PC AT with dual 5.25" floppy drives and a massive 20MB hard drive from an estate sale a few years ago that is in working condition.  I has the original "green screen" monochrome monitor and the "clicky" keyboard.  I recently picked up an IBM PS/2 with a 3.5" floppy and a tape drive (that is Personal System 2, not Playstation 2) which is IBM's replacement for the PC AT.

I don't have any rare/expensive console games, but I do have a lot of old PC games. Old PC games usually don't go for much (no one really knows their value which is why I collect them more then console games) but they are lot more rare then some of the more expensive console games. 

The rarest games I can think of off hand at this moment is the first is Suikoden 1, and the second one is Suikoden 2. Another rare game I have is Dragon Force for the Sega Saturn. An obscure game I have, is actually within that title I just referenced the Obscure game one and two. Those two games were quite different odd and scary at the same time.

Although it apparently holds NO value on Vizzed, I think Tunguska: Legend of Faith for PS1 is the most obscure video game I own physically. I dare you to find accurate info about the game on the internet. It seems like almost none of the internet has heard of this rare game.