The Dude and Rooster Cogburn probably wouldn’t get on too well…
I wonder what Frederick Treves would think of Hannibal Lechter
And I know H.G. Wells would despise Alex DeLarge
While Arthur Spooner and Frank Castanza are the same character, they would despise each other.
I don’t think Dick Solomon and Dr Emilio Lizardo would get along at all.
Oh - similarly, Dick Solomon and the Trinity Killer could even feasibly be colleagues, though Dick’s daftness would drive him so crazy that he’d risk including someone he knows as the Dad victim in his killing cycle.
There’s the problem that they live a century apart, but it would be interesting to watch an encounter between Dr House and Lt George.
Colonel Jack O’Neil and Tim Burton definitely wouldn’t get along. For one thing, O’Neil has no sense of humor, and Burton is kind of an idiot. 
William Thatcher may not care where the Joker got his scars, but I’m sure he could be pressed to add one or two if it came down to it.
They might work together well enough in the short term, but once they got to know each other, I can bet that Jim Gordon and Stansfield also would be at odds with each other. Similarly, I can’t see Sirius Black getting on so well with Jean-Baptiste Emanuel Zorg.
Jack Burton. :smack: