Banks is ok.. but I think he gets a little preachy sometimes, particularly when it comes to issues of religion (in Consider Phlebas anyway).
For fantasy, I think in addition to Tolkien (who essentially is the father of Epic Fantasy), I think Robert E. Howard and his Sword and Sorcery stories (specifically, but not limited to Conan) which pretty much defined the sub-genre. I am not a huge fantasy fan so I will limit my comments on fantasy to that.
For Sci-Fi... Childhood's End by Arthur C. Clarke, I Robot by Isaac Asimov, The Moon is a Harsh Mistress by Heinlein are all classics that should be read, even if they do occasionally show their age. Dune by Frank Herbert has aged very well (imho), but avoid the sequels (imho). Others I really like... Beggars in Spain by Nancy Kress, Ender's Game and Speaker for the Dead by Orson Scott Card, Forge of God and Anvil of Stars by Greg Bear, Startide Rising and the Uplift War by David Brin.