I know it's a clichéd choice, but New Super Mario Bros. is still my favorite DS game. Such platforming bliss, and so much personality in its presentation.
My favorite NES game is Ninja Gaiden. I love the cinematic style of the whole experience, and it's nice to have a bit of challenge every once in a whole :)
Hellyeah, I'm a huge fan of the older games; Super Castlevania IV and Symphony of the Night are my faves. Especially the former because of all the gothic outside scenery and incredibly smooth controls. :)