The OLDEST game? IF you count physically, I think I have the original cartridge for Super Mario Land, and Alleyway, which both came out with the Game Boy itself.
However, if you mean the oldest,
including virtual console games, well I believe that'd be the original Pac-Man, which came out in 1980, which is 5 whole years before Super Mario Bros.
However, oldest Nintendo game? Probably Mario Bros.
No, not Super Mario Bros, but Mario Bros, this one:
Although, then, if you also count games that are featured within games, then as a full game, that'd be 'Sheriff'.
Which is a Nintendo game which came out way back in 1979. Yes, 1979.
Although WarioWare has microgames based on really old Nintendo things, such as the Ultra Machine, while not a game, was invented by Nintendo way back in the late 1960s IIRC, but for games, I think the oldest game that's represented by a microgame, is probably Color TV Racing 112, which dates back to either 1978 or something.
But then, technically, Duck Hunt dates back to 1976, but it's just the NES version that came out 10 years later is more popular.
http://www.youtube.com/watch?v=YaUmcG3iors