And another British duo, Honeysuckle Weeks and Michael Kitchen in Foyle’s War. (Not romantic chemistry.) Also John Thaw and Kevin Whately in the Inspector Morse series, Geoffrey Palmer and Judi Dench in As Time Goes By, and Graham Crowden and Stephanie Cole in Waiting for God. (Gotta love PBS and BBC America.)
Seth Rogen and Paul Rudd (“Know how I can tell you’re gay?”)
Hugh Laurie and Peter Jacobson (Actually, Hugh Laurie and almost anybody, but Jacobson really held his own w. Laurie).
Alan Alda and David Ogden Stiers
Martin Sheen and Stockard Channing
Rowan Atkinson and Hugh Laurie.
Rowan Atkinson and Stephan Fry
In the Yes Minister episodes Nigel Hawthorn and Paul Eddington.
Emma Stone and Ryan Gosling in the movies they have been in togethe
And for a classic example Errol Flynn and Olivia De Havlinde
Colbert and Jon Stewart:
THOSE were the days when TDS was REALLY GOOD! 
Peter Cook and Dudley Moore.
John Thaw and Kevin Whately as Inspector Morse and Sergeant Lewis.
Kevin Whately and Laurence Fox as Inspector Lewis and Sergeant Hathaway.
Yes.
YES. The best example of “chemistry” I’ve seen in a long time. Also between Whately and Clare Holman.
Another outstanding example is from the Oscar winning Argentine film “The Secret In Their Eyes.” Soledad Villamil and Ricardo Darín are amazing together. The director even mentions it in commentary-- when filming began it immediately became apparent to everyone that something special was happening with the two actors.
Bert and Ernie.
It’s like they were made for one another.
Rowan Atkinson and Sir Tony Robinson
But John Belushi and Dan Ackroyd were pure magic together. The original Blues Brothers movie is still wonderful, so Jake & Elwood Blues also hold up.
Emma Thompson and Alan Rickman in Sense and Sensibility had such amazing chemistry it sort of screwed up the movie, given that they were supposed to be in love with other people.
Simon Pegg and Nick Frost in anything they’ve done together.
John Astin and Carolyn Jones as Gomez and Morticia in The Addam’s Family.
John Noble and Jasika Nicole as Walter Bishop and Astrid Farnsworth on Fringe.
Even though he almost never got her name right.
The all time champ with Hugh Laurie has to be Robert Sean Leonard. House & Wilson made the cover of TV Guide as the perfect bromance.
That should be #1. Their sexual chemistry practically melted my TV set.
Kate Jackson and Bruce Boxleitner in the TV series “Scarecrow and Mrs. King” (1983-1987).
Michael Richards and Wayne Knight as Kramer and Newman on “Seinfeld”. I was hoping they might get a spinoff when “Seinfeld” ended.
Kelsey Grammer and David Hyde Pierce as Frasier and Niles Crane. You could really imagine those two as a pair of brothers in real life.
And speaking of characters from “Cheers”: George Wendt and John Ratzenberger as Norm and Cliff.
George Clooney and Brad Pitt in the Ocean movies.
Saw a preview of Clooney’s new movie ‘The Monument Men’. Matt Damon is also in it.
Clooney’s chemistry with about anyone from the Ocean movies is great.
Roy Dupuis and Peta Wilson in the original La Femme Nikita.
From “Due South”, Paul Gross as Constable Benton Frasier and David Marciano as Detective Ray Vecchio.
As evidenced by the way the show went downhill after Frasier got a new partner. 
Homer & Marge
Stewie & Brian
Kermit & Piggy
Fred & Wilma OR Fred & Barney OR Wilma & Betty (but not Fred & Betty)
Samantha & Darrin #1 (but Samantha & Darrin #2? Not so much.)
Gomez & Morticia
Gilligan & the Skipper
Thurston & Lovey
Ginger & Mary Ann
Picard & Crusher
Jackie Gleason and Art Carney as Ralph Kramden and Ed Norton on The Honeymooners.
Add to that Audrey Meadows as Alice Kramden. Gleason originally refused to even consider her for the role, saying she was too young and pretty. She countered by anonymously sending him a photo of herself taken right after she had gotten out of bed, dressed in a bathrobe and holding a frying pan. He took one look at it and said “THAT’s Alice!”