This seems a very open subject, it's hard to know where to start. I'm going to be repeating a few recommendations already mentioned above, but I guess that might be useful anyway.
In no particular order my favourites include:
Harry Potter, J.K. Rowling.
Discworld, Terry Pratchett
The Chronicles of Thomas Covenant, Stephen Donaldson
Also in no particular order, honourable mentions go to:
Tarzan, Edgar Rice Burroughs
Cluster Series, Piers Anthony
Belgariad and Malloreon, David Eddings
Riftwar and Empire, Rayment E. Feist and Janny Wurts
Amtrack Wars, Patrick Tilley
Duncton Chronicles, William Horwood
Temperance Brennan, Kathy Reichs
Kay Scarpetta, Patricia Cornwell
Hercules Piorot, Agatha Christie
Constatin Vadim, Donald James (only three books but very good)
Artemis Fowl, Eoin Colfer
Sherlock Holmes, Arthur Conan Doyle
John Corey, Nelson DeMille
Dirk Pitt, Clive Cussler
Robots, Empire and Foundation, Isaac Asimov
James Bond, Ian Fleming
There are some it's tempting to put here (LotR and so on), but it's arguable as to whether they qualify as series (I first read LotR as a single very heavy book). Also the Gap books by Stephen Donaldson may be 5 books long, but it's more like one huge book than a series. Anyway, the above gives a reasonably diverse collection to pick from
.