I thought of that, but since the rhythm section is generally considered to be bass and drums, I didn’t. Also, Keith gets plenty of attention, while Wyman gets criminally little, so I took it upon myself to right a wrong.
The whole band had better make the music move forward, or you haven’t got much of a band.
More like: I was just trying to think of bands who can crank out groovy grooves that make me shake my ass, which makes driving difficult at times.
Hence the difference between “best rock rhythm sections” and “best rock drummers and bass players.” Paul McCartney and Ringo Starr’s names often come up on lists of great bassists/drummers respectively, but it’s no surprise to me that they haven’t been mentioned in this thread, I guess because Paul’s more melodic than rhythmic as a bass player, and because you don’t really think of them working together as a “section.”
Welcome to the world of being in a band 
What you are saying is actually not correct - by that I mean that there are three flavors of player:
ETA:
Auction Barn Messiah (great username, btw) - Larry Graham is a god. Definitely on the Mt. Rushmore of bassists
and NoCoolUserName? You hold up U2 as a great rhythm section with a lousy vocalist when I would argue that their weakest point by far is their rhythm section, but YMMV…
Jack Casady & Spencer Dryden
followed by, in no particular order:
John Entwhistle & Keith Moon
Charlie Watts & anybody
Paul & Ringo
Berry Oakley, Butch Trucks, & Jaimoe
That is exactly correct. I almost said the same thing.
Also, another vote for Bruford & Levin.
.
What? No love for Dave Hartman and Mary Huff?
I agree with the folk who have distinguished between best instrumentalists as opposed to best "rhythm section. I’m a bassist, and have been a HUGE fan of Rush, the Who, Queen, and more. Fantastic drummers and bassists to be sure. But in my mind, the strongest "rhythm sections are the ones where drums and bass work together as an unstoppable force, driving the music.
Billy Blough and Jeff Simon behind George Thorogood. The revolving cast in the Fabulous Thunderbirds. Those are the types of rhythm sections that make my heart stop. Unfortunately, guys who are just incredibly tight and solid tend not to end up as household names…
I wanna work where you do! I could talk about Stratocaster planning all MONTH and not get bored!
Is it too late to get on the Les Paul sub-committee?
César Bustamante (bass) / Jorge Durand - Arturo Creamer (drums) for Frágil (Peru)
Wouldn’t it be great if we could discussing “Strat” planning instead that pesky company strategy? I’d be all over it.
But you, my snowboarding friend, have no idea how much you’d want to join the meeting - its retreat being held in Vail, Colorado…
To the pain!
If I was being paid to be in Vail there is no way I wouldn’t hit the slopes. I’d do the bare minimum necessary for the job and then be out practicing my stuarts and shit. 
OTOH, I’ll prolly be kayaking on the Colorado while your in Vail… and it’s already warm here… mmmmmm sunshine.
Most of my favorites have already been mentioned, so here are a few outliers that came to mind…
Frantz/Weymouth (Talking Heads, Tom Tom Club)
Buckler/Foxton (The Jam)
Chambers/Farndon (Pretenders)
Morton/Steele (The [English] Beat)
Taylor/Taylor (Duran Duran)
Thompson/Taylor (Power Station)
Thompson/Edwards (Chic, but did tons of session work on more “rock” oriented acts)
Calhoun/Skillings, then Calhoun/Wimbish (Living Colour)
Hirst/Gifford, then Hirst/Hillman (Midnight Oil)
Berry/Mills (R.E.M.)
Chambers/Moulding (early XTC)
I had to think hard about this one, as I had a hard time figuring out if it was the band that I liked or the rhythm section proper… but I am at peace with it.
Headon/Simonon (The Clash)
(I see on preview that Bo already nominated The Clash… phew!)