Ice Climber - I would love to see a new Ice Climber game on the Wii/3DS. It only had three games, Ice Climber [1985] (NES), Ice Climber-e (E-Reader/GBA) and available as one of the "classic NES GBA games" (I cannot remember the title), all are based on the original NES game.
Startropics - I don't know much about this game and have never played this or the sequel; the last title was in 1994 - Zoda's Revenge: StarTropics II.
Clu Clu Land/Devil World - These were basically Pacman style games, I've played Clu Clu Land, but not Devil World. Of course, some elements from these games were incorporated into the Super Smash Bros. series; the unused Tamagon trophy in SSBM (which was removed in the PAL release), a Bubbles trophy and the inclusion of the Unira item and Devil assist trophy in SSBB. Neither Clu Clu Land or Devil World went relatively far, with the NTSC Devil World suffering partly because of religious concerns. Clu Clu Land has had three games; the original NES game (1984), Clu Clu Land: Welcome to New Clu Clu Land (1992) - a Super Famicom game (JPN only, but available on Animal Crossing as Clu Clu Land D) and a port "Clu Clu Land-e" of the original Clu Clu Land available for the Game Boy Advance as an E-reader game (2003). Bubbles is an unlockable character in DK King of Swing. Devil World has only had one game released in Japan for the Famicom in 1984 and Europe for NES in 1987. It was never released outside of Europe and Japan because of strict religious guidelines; RE: its inclusion of the Devil, the Bible and Cross. I don't even recall it making one small, minor cameo appearance except for the unused Tamagon trophy and Devil assist trophy in the SSB series.
R.O.B - "R.O.B games" included Gyromite and Stackup. I never played any of those games and never got a R.O.B, but it would be interesting to see remakes of the original games.
Balloon Fight - There was Tingle's Balloon Fight as late as 2007 but it was only available to members Club Nintendo [JPN], other than that the last game was Japanese exclusive Balloon Fight GB (2001), a graphically enhanced version of Balloon Kid (1990-1991). I've only had the chance to play Balloon Fight and Balloon Kid. Balloon Kid unlike the original Famicom/NES Balloon Fight was a side-scrolling adventure style game instead of an arcade-style game like the original. It was only released outside of Japan until the release of special edition Balloon Fight GB though there was an earlier Famicom version Hello Kitty World (1992), which replaced all the original Balloon Kid characters and some of the objects/enemies =/.
Drill Dozer - Released for the GBA in 2005 (JPN) and 2006 (US). It was never released in Europe. Rather nice gameplay, developed by Game Freak.
Duck Hunt - I'd like to see a Duck Hunt game on the Wii, but I don't know whether it would go too far.
Space Fever - A very early game series based on Space Invaders released by Nintendo in 1979 (JPN) and 1980 (NTSC). It would be interesting to see a revival of the series but it would probably be too similar to Star Fox and X. The series included a special edition "SF-Hisplitter" and there was one cameo appearance; a game called "Space Fever II" built into the Game Boy Camera (1998) and at the end of each 'stage' you would face a boss with one of the GameBoy Camera developer's faces or your own.
Probably deserves more attention outside of Japan
Starfy - There hasn't been even one Starfy game released here in Europe, not even the only NTSC title in the series, "The Legendary Starfy". Starfy has had three Game Boy Advance games and two DS games, with only the latest DS game being released outside of Japan (in fact even before the Japan release itself). Apparently the other games were rejected by Nintendo of America for being "too Japanese".
Earthbound - Last game was a port of Mother and Earthbound released only in Japan, June 2003 and re-released as a Value Selection game on February 2003. I'd love to be able to play at least one Earthbound game =[.
Captain Rainbow - Only released in Japan for the Wii (2008), is an adventure/action game.
Shin Onigashima - I don't know much about this game but it was rather successful, albeit a little hard apparently. Series has made various cameo appearances,
Sennen Kazoku - A life simulation game only released in Japan for the GBA (2005). Basically, by orders from God, Cupid watches down on a family. They will live on independently but their actions can be changed by firing arrows to change their emotions. The aim of the game is to keep the family going on for many generations to come. Rather strange, but I like the concept.
X - The original X was released for Japan in May 1992, gameplay is similar to Star Fox. A spiritual sequel, X-Scape was released in May 2010 for DSiWare. It is called X-Returns in Japan and 3D Space Tank in PAL regions.
Tomato Adventure - Developed by Alpha Dream and released for the GBA in Janurary 2002. The Mario & Luigi Superstar Saga game engine is based on this game IIRC.
Doshin the Giant - Released for the 64DD only in Japan with an expansion and later for the GameCube in 2002. A GameCube version was released in Europe but never localized for the US. A life simulation game with potential but reviews were mixed, it was a hit game in Japan but not so successful in the UK.