NES: Mega Man 1-6, Zelda 1-2.  Along with ~35 other NES games.

SNES: FF 2-3 (US versions, bought used for full price during SNES era), Super Mario RPG

Sega CD: Sonic CD, Eccho: Tides of Time

I doubt any of more recent games are rare at all so I won't bother listing them.

I think Mario DDR might be my rarest game........but I'm not sure if it meets your 2nd qualifier. I don't know too much about rare games.

      I don't think there is any way the two Ogre Battle games are as rare as Crazy Climber or SwordQuest:  Fireworld for the 2600.  Crazy Climber, in particular, was only sold to members of the Atari Club.

I don't know which ones I have are rare but you can look here and tell me and make my day. :-p

Also, just found I'm getting Earthbound back from my sister so that's one!

Swordquest is a dime a dozen, and worth much less than my Ogre Battles.

Crazy Climber on Atari's a different story though.

Grrrrrr....

&

And no, I am not selling those.

Chrono Trigger (SNES)
Vib Ribbon (PS1)
Super Mario RPG (SNES)
Panzer Dragoon Saga (Saturn)
Grandia (Saturn)
Seaman (Dreamcast)
Marvel vs Capcom 2 (Dreamcast)

wait.. aren't all dreamcast games rare?

I was looking through that link and saying "DAMN! His collection is like 100% the same as mine!"

I then realized it was my collection, lol.

OT: I am not 100% sure, although right off the top of my head I can guess.

Valkyria Chronicles (soon)

Tales of Vesperia (soon)

Valkyria Profile (PS1)

Lunar: SSSC

Lunar 2: EBC

Disgaea (PS2)

I probably have many, just check my game collection. Over 275 to pick from with many of my older titles yet to be added.

O yeah.. I forgot:
Final Fantasy 7 & 8.....the PC versions!!

and