The hard part of this is that series are never done.
Science Fiction
The Foundation Series, Isaac Asimov. The first three books only. This series was done for 40 years until he started writing them again, unwisely in my opinion.
The World of Tiers, Philip Jose Farmer. Farmer has several good series but I think this is his best (though equal parts science fiction and fantasy), followed by Riverworld (which falls apart at the end, in my opinion).
Dune, Frank Herbert. The first book is so good that the series has to make anybody’s list but all the books after the first suck.
Fuzzy Sapiens, H. Beam Piper. It is only two books but they are truly fun. Piper’s suicide was a great loss to science fiction.
Mission Earth, L. Ron Hubbard. I’ve only put this in here to see if anybody is paying attention. The first book actually sets up an interesting universe/idea. The following nine books proceed to destroy any shred of promise contained within the first book.
Current entry: Otherland, Tad Williams. Only the first three books are out and it is already shows signs of wear. It is showing potential, however.
Fantasy
Tolkein. I have never understood the fascination with these books. I enjoyed them as a kid but by the time I reread them as an adult they seemed too juvenile.
The Chronicles of Thomas Covenant. I think this series should be in anybody’s top five. Yes, most people find it too pessimistic but I think they are missing the point. However, the series manages to use all of the mainstays of epic fantasy without making them cliches. The Second Chronicles are weaker than the first three books but overall it is a fantastic series.
The Riftwar Saga, Raymond E. Feist. Feist has extended this series well beyond the stories useful lifespan but the first series is very good. (It isn’t a series but everybody should read Feist’s “Faerie”)
The Dragonriders of Pern, Anne McCaffrey. This one will gets lots of guffaws but I think if you consider only the early books it is a decent series (the downfall was trying to turn Pern into a Science Fiction universe rather than a Fantasy universe).
You all should know that I am printing out this thread. In recent years I have pretty much given up on Fantasy and Science Fiction because it was becoming increasingly hard to find something worthwile to read. It has been a couple years of mostly non-fiction. I am going to take each and every one of you up on your recommendations and see if you have any taste.