it varies from game to game, some you need more than one, but with others, you can do single card multiplayer,
single card examples
sure mario kart and brain traing do work with single card play, as well as others like:
diddy kong racing ds
mario party ds
zelda phantom hourglass
super mario 64 ds
metroid prime hunters ds
bomberman land 2 ds
tetris ds
plus many more
multicard games
pokemon diamond/pearl
custom robo arena
dragon quest monsters joker
animal crossing wild world
mario and sonic at the olympic games
42 all time classics
star fox command
and many more, all on the ds