The OP did specify franchise of 4 films or more. Of sci-fi films, that is. Consequently, that leaves out LOTR ... at least until "The Hobbit" comes out. Once that happens, all best are off.
Precisely. In fact, in my eyes, LOTR will win this
by default when "The Hobbit" comes out. It doesn't matter if that film is terrible (which seems less than likely to me), the Jackson triloy is in and of itself the best franchise achievement of sci-fi/fantasy filmmaking.
Besides that I'm sort of disappointed by the paltry showings. This world of 'franchises' is littered by would-have beens and coulda beens, and any franchise that goes on long enough varies preposterously much in quality. Just consider, say, the Godzilla series, which is probably the longest running sci-fi/fantasy film series. The awful, the mediocre, the dismal, the forgettable, and oh yeah, the cinematic classic people have been milking for generations.
King Kong also has enough movies to qualify (there was a sequel to the original film and also the 1970s remake, giving us five even if we don't count his crossover fight with Godzilla!) but who the hell wants to count that? Let us pretend that in 1933 when the Willis O'Brien stop motion gorrilla fell to the ground the story concluded that day and none would return to milk his tale for every dime it was worth.
So in the tradition of such latitude, I'm giving the mantle to Star Trek. It's got more than three movies I'd feel comfortable watching several times and are really damn good fun. Star Wars peaked with Empire and has been slipping ever since, despite a rather gaudy hiccup in 2005. An honourary nod and second place... to Batman, whose Burton and Nolan periods are pretty watchable, which means we've got three good movies and one which has good elements (Burton's first, if you're curious).
Also, wait, more people are bothered by
Temis dissing Batman than LOTR? I feel sad now. Cameron's comment about there being too many comic book movies seems more and more pertinent to me with each passing day.
Possible Future Best: Avatar. Yeah, I said it.
It's got definite potential, but not LOTR-felling majesty. We'll see.