The Fast and the Furious (2001-2015)
It started as a Point Break rip-off and has become one of the most successful franchises in history, grossing over $2.3 billion (not including part seven). After only the late Paul Walker stuck around for 2 Fast 2 Furious, and even he bailed on Tokyo Drift, a soft reboot brought the gang back together for Fast & Furious. But it was the inspired casting of The Rock as an antagonist to Vin Diesel in Fast & Furious 5 that really cemented this franchise. Even more spectacular stuntwork and bone-crunching fights (across London and Glasgow no less) saw Fast & Furious 6 incredibly out-gross each of its forebears.
Best entry: Fast & Furious 5

Saw (2004-2010)
Fittingly, it was Fast & Furious 7 director James Wan who created this monster franchise, although his involvement beyond the first part is limited to a co-story credit on the notoriously gory (even for this series) Saw III. Saw IV and Saw V are hopelessly muddled, with a sprawling chronology getting out of hand, before Saw VI surprisingly finds something interesting to say about the US healthcare system. The Final Chapter attempts to out-gross its progenitors, its reliance on 3D unnecessary and late to the party.
Best entry: Saw

Police Academy (1984-1994)
Due to a shortage of police officers, the mayor of an unnamed US city declares anyone willing to enlist must be accepted as a police officer. Cue a diverse band of misfits who mug around and fall about as they attempt to perform their duties. The series helped make a star (briefly) out of Steve Guttenberg and featured early roles for Kim Cattrall and Sharon Stone. More than any other film series, Police Academy accurately follows the law of diminishing returns.
Best entry: Police Academy

The Texas Chainsaw Massacre (1974-2013)
Tobe Hooper's original is a foreboding and desolate horror masterpiece. A group of teenagers are picked off by a chainsaw-weilding maniac (named Leatherface), part of an oddball family very loosely based on notorious serial killer (and Psycho template) Ed Gein. Hooper's own sequel upped the gore and turned it into a black comedy (featuring a chainsaw duel between Leatherface and Dennis Hopper). Renée Zellweger and Matthew McConaughey no doubt wish they could strike off The Next Generation from their filmographies. A so-so reboot and prequel followed in 2003 and 2006, produced by Michael Bay's horror remake outfit Platinum Dunes. Texas Chainsaw 3D gets confused by its own timeline.
Best entry: The Texas Chain Saw Massacre (1973)

A Nightmare on Elm Street (1984-1994)
In a decade filled with formidable horror characters, Wes Craven created possibly the most iconic in the guise of child murderer Freddy Krueger (named after a kid at school who had bullied the young Craven). The original film was tremendously influential and spawned a slew of poor sequels (including the execrable Freddy's Revenge). Annoyed at the cliché Krueger had become, Craven returned to re-examine his creation in Freddy's Dead: The Final Nightmare, as a warm up for his fascination with post-modern horror (see the Scream franchise).
Best entry: Nightmare on Elm Street

Ju-on (The Grudge) (1998-2014)
Takashi Shimizu's Ju-on series rode high on the wave of late 90s/early 2000s Japanese horror (see also Ring, Dark Water and One Missed Call). In the Ju-on series, evil spirits are created in dwellings when a person is murdered. The US film The Grudge (also directed by Shimizu) is (confusingly) a remake of the third in his original series.
Best entry: The Grudge

X-Men (2000-2014)
It's easy to forget what a gamble the first X-Men film was. And it wasn't until Spider-Man took $821 million that studios (and Marvel in particular) really took notice. X-Men 2 outstripped its predecessor's box office by doing what all good franchises do: it went darker. Director Bryan Singer stepped down and was replaced by journeyman Brett Ratner for the turgid misnomer X-Men: The Last Stand. Two attempts to place Wolverine front-and-centre faltered before Matthew Vaughan breathed some life into the franchise in the 60s-set First Class. Singer returned for Days of Future Past and is behind the lens for next year's X-Men: Apocalypse.
Best entry: X-Men 2