The two NSA agents played by Hank Azaria and K. Todd Freeman in Grosse Pointe Blank are sort of a marriage of this trope and the traditional Salt and Pepper buddy cop pairing. Martin Q. Blank (John Cusack) and Grocer (Dan Aykroyd) also fit somewhat, although they are rivals.
The pirates Pintel and Ragetti from Pirates of the Caribbean, who happen to have good guy counterparts in the Royal Navy, Mullroy and Murtogg who are just as much twits albeit much more gentlemanly and well-behaved. By the third film, things become murkier, because while their personalities remain the same, Mullroy and Murtogg are enlisted with rest of the Marines into the new Big Bad's national-private army while Pintel and Raggeti work in the same team with the protagonists out of self-preservation.
Mr. Frying Pan and Mr. Fire from Kiss Kiss Bang Bang. (Their actual names aren't given, but this is what they are listed as in the credits.)
Going off of the Men In Black reference above, those characters in general have a similar dynamic as this type of character, and the Agents are a particularly good fit. There's three of them instead of two, but that hardly matters.
The Twins from the The Matrix Reloaded probably also count. While they don't really exposit much, they do provide some amusing dialogue, talking to each other in an unconcerned deadpan while being shot, and taking part in a highspeed car chase.
Sydney Greenstreet and Peter Lorre were sometimes teamed up this way after The Maltese Falcon. Subverted by their cameo in Hollywood Canteen, where after Lorre asks a man if he "would like to step outside for a moment", he innocently tells Greenstreet "I was only going to ask him if he wanted a cigarette".
MasterBlaster, the duo who run Underworld in Mad Max: Beyond Thunderdome ("They are a unit; they even share the same name"). Master is a mental giant with a body like a small child's; for Blaster, the reverse is true.
Possible Real Life example: Burke and Hare. Their cinematic versions in 1960's The Flesh and the Fiends definitely fit (and Donald Pleasance is particularly Faux Affably Evil as Hare).
Peter and Paul from Funny Games, most definitely. Although they are not as comical as you'd expect them to be (and Paul is more the brains and the dominant one, while Peter is his considerably less intelligent and more passive sidekick, they are every bit as bantering and bickering as the typical examples (which makes them a bit humorous given Paul's sardonic comments and Peter's whiny retorts) and make a great, murderous team of sociopaths.
The Wet Bandits in Home Alone are another duo of main antagonists who act on their own initiative rather than following orders and yet have contrasting looks and personalities.
Mr. Wint and Mr. Kidd, in the James Bond movie Diamonds Are Forever, possibly the Trope Codifiers. (Quite a few other examples listed here are based on them, at least partially.) They have a strange habit of dispatching everyone else in the diamond smuggling ring and tried to off James Bond three times: once by leaving him to meet a fiery end in an incinerator; again by leaving him to rot in a pipeline; and the third and final time by appearing to him in person disguised as the cruise ship's kitchen crew.
Snatch.: Bricktop has a pair of thugs, Errol and John, who function like this.
Agent Johnson and Agent Johnson, from Die Hard, count, even if they're not technically bad guys.
Howard and Eli from the Video Violence duology.
The Joss Whedon / Drew Goddard film The Cabin in the Woods has Hadley and Sitterson, who provide much of the film's humor as well as its most interesting characters. It helps that 1) they stand out as non-fighters who actually co-ordinate attacks from behind computer screens, 2) that they are witty and funny which, given their aforementioned lack of action jobs, they get to display on lots of occcasions, 3) they feel more like your typical run-of-the-mill work-place executives rather than the run-for-your-life senior executioners.
Leonard and Willie (Damon Wayans and Kadeem Hardison) in I'm Gonna Git You Sucka are two bad guys who work for Mr. Big and spend the movie trying to kidnap and murder, but they are mainly idiots. One is dumber than the other... but only slightly. They always end up getting beat up and having to decide between going out the window or down the stairs.
Alec Pearce and Vernon Crump from The Titfield Thunderbolt. They are the owner-operators of the local bus company, and the closure of the Titfield branch line would mean a transit monopoly for them. As such, they are determined to undermine the effort to preserve the line.
In Jo, Leduc and Grand-Louis, who comes to fetch Riri's money, and thanks Antoine Brisebard for having done the dirty work in their place by accidentally killing Riri.
Lucky Number Slevin has two sets of these. The protagonist meets Elvis and Sloe first, who practically invoke the trope. He later meets Saul and the Mute, who subvert the trope in that one of them is a mute, so any exposition is given directly to the main character.
The Comedy of Terrors: Mr. Trumbull and Mr. Gillie partners in crime trying to keep the mortuary business running.