Well, of course there is nothing like Harry Potter! But there are some fantasy series (usually shelved with Science Fiction) that deal with young people struggling to learn magic or to control their magic powers. Here are some I liked
Rhapsody (Book 1) Prophecy (Book 2) Destiny (Book 3) by Elizabeth Haydon
Any of the Valdemar Series by Mercedes Lackey (there are a TON of them- most written in groups of 3)
The Magician series by Raymond E. Feist. First one is Magician: Apprentice
Also, if you don't mind venturing into the children's department, there are some terrific series competing with Harry:
The Artemis Fowl series by Eoin Colfer
The Spyderwick Chronicles by Hollly Black
The Bartemeous Trilogy (only the first 2 are published)
Eragon by Christopher Paolini
Hope that helps!I love 'em all!