Why were these guys considered so great? I’ve never been one of those people who evaluate groups on how technically brilliant the playing is, but The Clash sound like first-year guitar students. And those ragged vocals!
They did have some ragged stuff, such as Should I Stay Or Should I Go (which I personally can’t stand), but they had a lot of stuff that was very well done technically. Rock The Casbah had the ragged voice, but was otherwise very produced. Excellent examples of songs which were pretty smooth in both voice and music include Safe European Home, Spanish Bombs (one of the best rock songs ever), Train In Vain, and Lost In The Supermarket (though the bass is clunky in one section).
Just a matter of personal taste. I feel the same way about Pavement, which is apparently sacreligious to some folks.
Either you like The Clash or you don’t, pretty similar to the entire Punk scene, though they were always a bit different than the rest.
I WORSHIP them 
— G. Raven
You know, as much as I adore The Clash, I think that London Calling is one of the lamest songs of all time. I mean, that stupid fanfare bass line (du-du-du-DUM) just kills me everytime.
Lost in the Supermarket is definitely a showcase of talents. To appreciate The Clash you have to take them as a whole and not look at individual songs. Try to realize what they were about and how they were trying to get their message across (Know Your Rights, Koka Kola, Death or Glory). Also look at the volume of their work in a relatively short period of time and most of all the, variety of their work - from reggae to rap(ish) to straight punk, to rock-and-roll.
I also strongly suggest Rancid (esp. Life Won´t Wait - very similar to London Callsing IMHO) for Clash fans. Rancid is similar in style and method as well as influences.
NP: Sepultura - Nation
Thanks to everyone who’s replied so far. Your answers have helped.
I just happened to hear Should I Stay and wondered what the whole brouhaha had been about. God knows I don’t automatically abjure bands because they’re not instrumental whizzes: probably my favorite group is The Doors, and their guitar player basically just got by technically (though I admire him for what he was able to create given his limited playing experience).
The whole brouhaha is just that… “whole”. Opengrave is so right. The Clash have some pretty mediocre songs, but when you look at their stuff collectively, it’s amazing.
That said, The Clash are one of my top five favorite bands. They were before my time pretty much, but I grew up with them.
Where’s London_Calling when you need him?
To some of us like me, a dedicated DCHC fan, the success of The Clash gave a lot of people hope that popular success could follow in the footsteps of critical praise.
For most bands, it didn’t.
Put The Clash in perspective: Reagan, Thatcher, Mulroney, rampant unemployment… Listen to their song “White Man in Hammersmith Palais” – it all makes sense.
And don’t worry if you don’t like SANDINISTA! or COMBAT ROCK. They sucked. 
Yeah, “Should I Stay…” was pretty lame, as was most of Combat Rock and much of Sandinista!, as wumpus pointed out. In the words of Too Much Joy:
“Every great band should be shot
Before they make their Combat Rock.”
That being said, at least the Clash tried to progress and didn’t just stay stuck in the “1,2,3,4” punk ghetto (not that I’m being judgemental; their first album is my favorite). London Calling alone encompasses punk, classic rock, reggae, pop, soul, piano ballads, etc.
As for the “ragged” sound, that’s part of the appeal. When punk first came out, the airwaves were full of long, bloated “superstar” rock songs with endless solos and rhythms stuck in the late 60s. Punk was a reaction to all that, an attempt to bring the music back down to earth. The Clash were one of the best at it, and will always be one of my top 5 bands.
Besides, who else would write a song about Montgomery Cliff (“The Right Profile”)?
(My favorite band too, from “London Calling” to the first half of “Sandanista.”)
I knew I liked you! 
::throws an egg in Pavement/Steven Malkamucous’s general direction::
[butthead]
Oh yeah, and the Clash, like, rule or something.
[/butthead]
Why, R.E.M., of course! “Monty Got A Raw Deal” is one of my favorites off “Automatic For The People.”
Because they are the only band that matters. The ragged vocals made the band. Strummer would have to make my list of top rock singers of all time. Jones too would be right up there. Plus Hey give them some credit, they were at least second year quitarists when they started out.