^ Great, keep them coming!

Hotel Dusk: Room 215

Chrono Trigger!

42 All-Time Classics
Age of Empires: The Age of Kings (or Age of Empires: Mythologies)
Anno 1701 (or Anno: Erschaffe eine neue Welt)
Another Code
Broken Sword: Shadows of the Templar (Baphomets Fluch)
Civilization Revolution
Dragon Quest IV (Chronik der Erkorenen)
Dragon Quest V (Hand der Himmelsbraut)
Dragon Quest Monsters: Joker
Final Fantasy IV
Final Fantasy XII: Revenant Wings
Rune Factory: A Fantasy Harvest Moon
Fire Emblem: Shadow Dragon
Meteos
Might & Magic: Clash of Heroes
Mystery Case Files: MillionHeir
Ninjatown
Picross DS (or Picross 3D)
Puzzle Quest: Challenge of the Warlords
Planet Puzzle League
Kirby Power Paintbrush
Mario & Luigi: Partners in Time
Mario & Luigi: Bowser's Inside Story
Scribblenauts
True Swing Golf
Zoo Keeper

Great games which I can't recommend for your library as they're only available in English:
Chrono Trigger and The World Ends With You.

Thanks guys, that's a lot to consider. I'm going to update the list tomorrow.

Seriously, Hotel Dusk is a must.

It's on the list now ^_^

Oh my gosh. Scribblenauts. I love that game. The best part is that it is a puzzle game based on words. It is perfect for a library.

Metroid Prime Hunters
Sonic Rush
Yoshi Island DS
Jam With the Band

Best Bets

New Super Mario Bros Wii
Nintendogs
Brain Age
Mario Karts DS
Animal Crossing: Wild World
LoZ: Phantom Hourglass
Final Fantasy 3
Pokemon Diamond and Pearl
Professor Layton (very popular in Europe I hear)
*Personal Trainer: Cooking (This is for a library, so having a cooking guide game may be a good fit)
English Training: Have Fun Improving Your Skills

*May be called "Cooking Guide: Can't Decide What to Eat?"

From there it gets sketchy. Other good picks
Rhythm Heaven (Good music game. Easy to get into)
Warioware Touched (fun minigame collection)
Tetris DS
Kirby Super Star Ultra (Again, another good platformer)
Mario & Sonic at the Olympic Games
Sonic Rush (see Kirby, but with Sonic)
Cooking Mama
Big Brain Academy
Mario & Sonic at the Olympic Games

Now, the top list are the ones I think you defiantly need to get. They are the most popular games on the system and will yield the best results. The ones below are also good choices, but are secondary. One thing you may want to consider is to get multiple copies of games that are really popular such as New Super Mario Bros and Brain Age. Also, Pokemon and Nintendogs have multiple versions, so maybe you want to get one of each (get Pearl and Diamond or Labs and Chiwawa and another). This way, people are not limited to one version. Another idea is also looking into other games in the series of popular titles, like maybe another Layton game or another Brain Age game.

Lastly, be careful of the comments here. Not to bad mouth anyone, but people are giving some request that are niche titles and may not be as enjoyable the people who will be looking at these titles. Elite Beat Agents is one (as much as I love that game). Avoid picking titles that a few people like. Be broad. If you have left over cash, go for more of one title, other version or others in the series.

What is the price of a DS game in your country? (Germany right?)