I clicked the 'Fantasy' tab because, of the two, that's the one I read most. But I do read some SF as well - Greg Bear, Peter Hamilton, Asimov and others. I'm never quite sure why the two are lumped into one genre, because to me they are completely different. As someone else said above, SF is the art of the possible, or even probable, but fantasy is exactly that!
I can't say I have a favourite fantasy author, since my favourite book is usually the last one I read! But I loved the Robin Hobb Farseer series (but not the Soldier Son Trilogy), also Guy Gavriel Kay (Fionavar Tapestry & Ysabel), Raymond Feist, K J Parker, L E Modesitt (Corean Chronicles) and heaps of others!
I'm just about to start Game of Thrones, 1st in the Song of Fire and Ice series by George Martin. I haven't read any of his stuff yet so wish me luck!!