Cousin It and Cartman
Mr. T and David Banner. I pity the fool.
Dr. House, and Dr. Cox from Scrubs.
FTW.
Cousin It and Kenny.
The Robot from Lost in Space and Bender
Herbert T Gillis and Archie Bunker, two veteran’s from W W 2… The Big One- with the good conduct medal and sons (in law) who don’t appreciate hard work
Dr. Harrison Wells from Earth 2 (The Flash) and Missy (Doctor Who).
I’d like to see Frank Pembleton and Captain Holt (Andre Braugher’s character from Brooklyn 99) argue, too.
Leslie Winkle and Gregory House.
Helena from Orphan Black and the cast of Seinfeld. The argument wouldn’t last long.
Teal’C and Worf
Red Reddington and Dr. Who (Capaldi)
Red typically charms people while marking their value to him and diagnosing their vulnerabilities. The Doctor usually relies on stupefying people with his brilliance and then herding them along for a wild ride. Red wouldn’t fall into that trap, but would try to lure the Doctor into his. The Doctor would totally discombobulate whatever Red had in mind through sheer chaos. Red would consider the Doctor a magnificent prize to capture and cheerfully move onto the next dance and make the stakes deadlier. The Doctor would be determined to win the battle of egos and turn the dance into a mosh pit. Lawful Evil vs Chaotic Good. They would be lifelong frenemies.
Garak and the Cigarette Smoking Man.
Awesome. Wouldn’t be surprised if it wasn’t actually an argument.
And if Red from The Blacklist happened to stop by…
And on The Flash, Harrison Wells from Earth 2 and Captain Cold.
Face (from The A-Team TV show) and Neal Caffrey (from White Collar).
Cage Match: Richard Castle vs. Maddie Hayes vs. David Addison vs. Kate Beckett
Heh. Yeah, maybe, but it’d be a hell of an interesting, sly conversation.
Dr. Cox vs John Larroguette
Off a cliff, with a pause for a second before falling?
Hee. You just reminded me of one of my favorite exchanges with my Mom. I mentioned how a friend was naming her pets after favorite TV shows (Xena, Buffy, etc.) and Mom pipes up “How am I supposed to name my pet ‘Homicide: Life on the Street’?!” 
“Mom, how about something like ‘Pembleton’?” So my hypothetical pug is named Pembleton.
Maybe House up against Romano from ER?
Not exactly arguing, but I’d like Capaldi Doctor to jam with Bill & Ted’s mentor Rufus.