My favourite series, heads and shoulders above the rest, is Lloyd Alexander's "The Chronicles of Prydain". They're children's books, but they stand the test of time incredibly well. The last time I read them I was twenty, and at that point I hadn't read them in about five years. I enjoyed them as much as ever, in some ways even more, because I was able to see the underlying themes more clearly than previously. I'm trying to read them with my little sister now, but when it comes to reading English is very much a second language to her, and we're having trouble finding some of the books in Hebrew, so it's going rather slowly.
I also love Terry Pratchett's Discworld series.
When I was small I loved Enid Blyton's Faraway Tree stories.
I very much enjoyed the "The Dark Is Rising" series, which someone mentioned somewhere in this thread.
I loved the Hitchhiker's Guide to the Galaxy books.
I enjoyed the Narnia books when I first read them, but I never considered them among my favourites.
The same goes for the "Anne of Green Gables" series.
I read the Sweet Valley Twins/Kids/High/et cetera books when I had nothing better available, but I always thought they were rather silly.
I was addicted to the Baby Sitters' Club books for a couple of years, but they had one problem: when I was ten years old they were thirteen years old. When I was thirteen they were still thirteen. At that point I stopped liking them, because what girl wants to read books about younger girls?
The only television tie-in series I enjoyed was the Babylon 5 Technomages trilogy, which I thought was better than the actual TV series.
If Marion Zimmer Bradley's Avalon books can be considered a series I'd have to include them here, although I have to admit they're a bit hit-and-miss.
_________________________
"Talk is cheap, arms are not"- Victor Davis Hanson