This is classic side-scrolling Mario Bros action, a successor to the original Super Mario games. The new moves in this one include a super-mushroom that turns Mario into a giant. Mario's adventure spans both screens.
You could start your DS collection with New Super Mario Bros., which is as fundamental as it gets, but try this twist inside. Mario & Luigi: Bowser's Inside Story is the newest in the series of creative role-playing games starring Nintendo's famous brothers and their wonderful cast of friends and enemies. This game has exploration, tons of inside references to past Mario games, more of the series' top-flight comedy (this is a rare game that will intentionally make you laugh), plus, it's got a twist: You play as Bowser in the top screen and you play as Mario or Luigi — who have been swallowed by Bowser — in the lower screen, exploring his, uh, guts. Read Kotaku's Mario & Luigi: Bowser's Inside Story review.
Think of a noun that describes something solid. Write it into the DS. That will make it appear in the DS as a person, animal or object that will hopefully help you solve one of the many puzzles in Scribblenauts. Maybe the way to get the star out of the tree involves a "tiger"? "hot air balloon"? "black hole"? "god"??? Read Kotaku's Scribblenauts review.
Pop music plays as Elite Beat Agents requires you to rhythmically tap and swipe at the DS' lower screen. Doing this and doing it well allows the game's feel-good heroic male cheerleaders to improve the lives of regular people, that turn of good fortune depicted through hilarious comic-book-style scenes on the DS' upper screen.
Puzzle Quest DS combines the match-three style of gem-matching puzzle gameplay popularized by hit computer game Bejeweled with the story, battling and character-leveling aspects of a good old-fashioned fantasy role-playing game.