Harry Potter is one of them of course. I also like The Empire Trilogy by Raymond E Feist and Janny Wurts, the trilogy is part of Feist's larger Riftwar Saga series. There's the classic Oz series, though I haven't read all of them. The Fear Street Saga by RL Stine (there's a trilogy: The Betrayal, The Secret, and The Burning) is one of my oldest favorites. I like several series within the Star Wars expanded universe; mainly The Thrawn Trilogy, the X-Wing series, and most of the Jedi Apprentice series. Lastly the Sword of Truth Series by Terry Goodkind and for a more loose series (they're stand alones, but fit together) Phillipa Gregory's Tudor books; The Other Boleyn Girl, The Queen's Fool, etc.
I also like the Vampire Chronicles, though I've only read Interview with the Vampire and The Vampire Lestat; and the Anne of Green Gables series, which I haven't quite finished.
A newer series that I may end up liking is The Imager Portfolio, as I really enjoyed the first book Imager, but I haven't gotten the 2nd book yet.