You might try some of the Ender's Game books by Orson Scott Card (definitely try
Ender's Game if you haven't read it); I enjoyed what I read, but I found couldn't finish the series.
Ooh! The
His Dark Materials trilogy by Philip Pullman, recommended with much urgency and no reservations. (Look for The Golden Compass, The Subtle Knife, and The Amber Spyglass, in that order.) This may be a good chaser to series like Harry Potter or Twilight.
Also, though it's not technically a series, because it's so long and the characters are so appealing, I found myself mourning the end of
Cryptonomicon by Neal Stephenson as if I'd just lost a lot of good friends in a bus accident.
Then, there's always Douglas Adams...