Some really good multi player games are Mario Kart, can be played with one cartridge up to eight players at once or multiple cartridges.
42 All Time Classics, loads of simple card and board games ideal for journeys as they can be a quick blast or a longgame such as chess.
Mario and Sonic at the Olympics, Cooking Mama, Animal Crossing, Nintendogs and Big Brain Academy are all brill games.
The thing to look for is on the back of the box. It will say multi card play (each player needs a copy of the game) single card download play (only one card is needed) or a combination of the two. Then underneath this is a number 1-2, 2-4, 2-8 which gives the number of players the game supports.
If the box doesn't indicate this it is usually just a one player game. Before deciding whch games to buy, check out a few game review websites and see what other people think. Here are some I use to check out a games reputation.
http://www.neoseeker.com/Games/Nintendo_DS/
http://uk.gamespot.com/ds/index.html?tag=nav-t op;ds&navclk=ds
http://uk.ds.ign.com/