Surprised there has been so very few posts in here, it's a good idea for a thread...is it ok to go for 3 if you can think of one...
The Blues Brothers/Ghostbusters/Groundhog Day
has the connection of Ackroyd starring in and co-writing the first two, then Ramis and Murray connection for the 2nd and 3rd.
Sin City/300 - Frank Miller double bill
Watchmen/V for Vendetta - Alan Moore double bill
Unbreakable/Kick-Ass - both deal with a world without superheroes that then gains them through folk reading too many comics.
Barfly/Factotum - Bukowski double bill, one an original screenplay by Bukowski, the other based on his novel 'Factotum', they actually have the same scene in them both, as Bukowski used incidents from his own life in both stories. Also, it is kind of funny as Mickey Rourke plays Chinaski in Bf, and Matt Dillion plays him in Factotum, and they were brothers in Rumblefish, kind of like the big bro passing on the mantle to the little bro.
Speed/Crank - two nice wee movies about people who cannot slow down for any reason.
Deliverance/Southern comfort - backwoods craziness, city types fight against the inbreds.
First Blood/Copland - Stallone fights against the small town cops, then Stallone becomes the small town cop fighting against the big city cops. Mindblowing role reversal switchover!
Falling Down/Taxi Driver - two crazy vigilantes, two crazy movies. 'You talkin' to me? Now you're going to die there wearing that little silly hat.'