If you're into fantasy, then you should start with the series from Hayao Miyazaki
http://en.wikipedia.org/wiki/Hayao_Miyazaki
There are dozens of genres out there, so you can be a bit more specific. Do you like "out of this world"-fantasy, or "fantasy mixed with reality".
The more "apocalyptic mood" or the "cheerful" ones?
Actionpacked, or romantic?