If you want epic fantasy, I highly recommend Stephen R. Donaldson's "Chronicles of Thomas Covenant, the Unbeliever". Absolutely awesome. There are two trilogies. The first book in the first trilogy is "Lord Foul's Bane". Don't be put off by the title...they are very well written books. SRD also has a good collection of short stories, "Daughter of Regals".
Another trilogy I would recommend is Guy Gavriel Kay's Fionovar Tapestry. I believe the first book is titled "The Summer Tree". The Fionavar Tapestry brings in elements from several mythologies. He also has a stand alone fantasy titled "Tigana", which I would rank first of all the recommendations I'm making here. Tigana is simply beautiful. I loaned it to one fellow at the office, & he felt it was one of the best books he ever read.
Greg Bear's "Songs of Earth & Power". Very original...very good.
Larry Niven is good for hard core science fiction, & he also has some fantasy.
Roger Zelazny, recommended above, is one of my all-time favorite authors. He is the master of the short story. In some of his books he brings in a bit of Hindu mythology...Lord of Light...Creatures of Light and Darkness...Jack of Shadows....& of course the enjoyble Amber series. Several short story collections. All good.
I really could just go on and on...
but...oh why not!
Louise Coopers Time Master Trilogy...Book 1 is "The Initiate". These are out of print, so you will have to browse the used book stores, but worth the search. The battle between Chaos & Order.
Barbara Hambly...The Darwath Trilogy...starts with "Time of the Dark". Very original. You can see her develop with each book.
Oh my goodness!!!! How could I forget...Kathryn Kurtz' Deryni Series. There are now 4 trilogies plus the most recent volume. I have been reading these for years. A bit beyond the middle ages epoch, perhaps, magic, sort of a scottish type of environment. Very, very good.
I really should stop now...please don't encourage me