That's tough because sixth graders are just slightly young to get into some of the seriously character-building stories like "To Kill a Mockingbird" or "Lord of the Flies".

Here are some that come to mind for sixth grade or earlier though:
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"Huckleberry Finn" or "Tom Sawyer" by Mark Twain, to understand race, culture, and have a foundation for knowledge of Twain's works

"Roll of Thunder, Hear My Cry" by Mildred Taylor to understand facing adversity, having courage, and racial themes

"Are You There God? It's Me, Margaret" by Judy Bloom to understand developmental changes, religious differences, and adolescent dilemmas. (Best for girls)

"Little Women" by Louisa May Alcott to understand the history of the Civil War era, and the importance of family

"The Wonderful Wizard of Oz" by Frank L. Baum to understand and embrace fantasy, while learning to recognize parallels between the fantasy land and the real world, and explore virtues of human character and the value of friends and family.

"The Little Prince" by Antoine De Saint Exupery to, again, understand worlds of fantasy and to emphasize the importance of creativity and resourcefulness

Basically what you're looking for is a mix of fantasy stories and tales that bring the real life into perspective. Learning to deal with harsh realities of life while still embracing creativity is a thin line that children AND adults have to walk. All of these stories, and more, help to sculpt childrens' character so that they can find that perfect balance and become the well-rounded people we want them to be!

As much as possible! I'm not going to give a list, because every 6th grader is different, and the books I found awesome at that age (The Westing Game! OK, I went back on my promise, but that book is amazing and has great characters.) might not seem to awesome to others.

I would try to encourage books with a bit more substance, though. A lot of young adult books these days are just product placement-laden ways to sell kids shopping and shoes (the ones marketed to girls) or gross-out humor (the ones marketed to boys). And while I've heard the argument that they're just "stepping stones," it doesn't always work out that way.

And above all things, stay away from Twilight! Abusive, controlling, stalker boyfriends mixed with unfortunate implications about sex? No thanks.

I am a language arts teacher, and I have found 6th grade to be the opening door to great literature. I have found the the classics are still a little unreachable for early middle school, but when they get really involved in a few good novels for children, they tend to take off on their own. Here are some of my favorites for 11-12 year olds:

Out of the Dust
Maniac Magee
Rules
Maximum Ride Series
Daniel's Story
Julie of the Wolves
The Whipping Boy
Sing Down the Moon

Anything that's not horrible teen fiction(Twilight, Harry Potter, etc)