Well as the tittle says really. XD Lets find some great book series. I'd be inclined to personly say "The Dark Tower" series by Stephen King, although I've not read the complete series yet so I can't say for definate. No-one give any spoilers!
The Faraway Tree Stories by Enid Blyton or Little Women, Good Wives, Little Men and Jo's Boys by Louisa May Alcott or do the Hardy Boys count as a series or are they a syndicate?
ok Then Hardy Boys win - they are still being written and there are hundreds of stories lol However I am not sure they should count as they have dozens of authors writing them.
Probably Steven Erikson's Malazan books at this point. Though if we're counting a shared universe as a single series, maybe the Warhammer 40K books, just for the sheer fun of them