Some picks off the top of my head:
Black Jack: This Osamu Tezuka manga is perfect for a library. It's basically an anthology plot structure; most of the stories stand on their own. It's hard to put down but every long chapter is its own self-contained tale. Most importantly, it's some of Tezuka's best storytelling, consistently entertaining and often thought-provoking. If I had to hand somebody one Tezuka manga and only one to read, right now it would be this.
Cross Game: Sports + character-driven drama collide here in what has been a very sincere, down-to-Earth manga with a healthy sense of humor. I've adored it and Viz's release has left me wanting more of Mitsuru Adachi's stuff. You could see a couple episodes of the anime on Hulu to get a feel for it (disclaimer: you may not want to stop). The last volume comes out in July.
Kimi ni Todoke: This is still being released. The anime was the sweetest shojo romance I'd ever seen, and it's also a positive story about an introverted teen coming out of her shell. Lots of humor too. This is better than Fruits Basket.
Story of Saiunkoku: It's also still being released. The anime was critically panned here, but I liked it and from what I've read so far, it actually does make a better manga.
Dragon Ball, Sailor Moon, One Piece: We both know why. I'm guessing your library has at least one already. Alternatives to Sailor Moon could be Magic Knight Rayearth or Sakura Hime: The Legend of Princess Sakura, a pretty well-received series that began in 2008. But I think any good collection is first built on a foundation of classics. I doubt your library has the old SM books, and the new print run is better anyway.