I think Top Thrill Dragster or Kingda Ka, simply because of the iconic shape and the fact that they both have been advertised as the tallest/fastest coaster in the world for some time. People tend to confuse one for the other, but they always tend to have heard the name.
Dueling Dragons is also so iconic that everyone seem to know about "the ones in Florida that nearly crashes with the other", though nobody knows the name.
Yeah, it's gotta be Cyclone or Space Mountain (or I guess BTMR).
Although I heard somewhere that Santa Monica West Coaster at Pacific Park is the most photographed coaster in the world. It really is in lots of commercials.
For the UK, I reckon its probably Oblivion. Everybody seems to know that ride.
As for the world, I'm going to go with Dueling Dragons too. A lot of people know about it because of it being unique and a lot of people go there. Space Mountain for a similar reason that its at a Disney park, so a lot of people will have been on/seen it.
Then again, I suppose TTD and Ka are pretty famous too.
Interesting question. Space Mountain is a likely choice for most well-known internationally. As for Oblivion, I'm sure virtually nobody outside of the enthusiast community in the US is aware of it, though the same can likely be said for the European public's awareness of KK/TTD.
Within the US, the most well-known coaster has got to be either Space Mountain, TTD, or Batman: The Ride since it's at pretty much every Six Flags Park.
It doesn't matter if people can't tell you exactly what it is, most people know where it is etc.
How many times do you hear Duelling Dragons references on TV? It's always Space Mountain... That's how I think of it. Which rides are talked about most by characters on TV shows? Over here it used to Alton, but, it's becoming Thorpe, and Worldwide... Disney/Space Mountain.
Matterhorn/Space Mountain are definitely at the top/near it. Other than that is Desperado at Buffalo Bills Casino. Hearing everyone who comes from LA and is going to Vegas always talks about "that huge roller coaster at state line!"
Those are probably the three biggest though, I might say Matterhorn wins just because it was THE simple for Disneyland before they expanded outside the U.S. but since it is Space Mountain.
Seems like Desperado is really only known by people who've passed it or ridden it, though. I've never heard anybody out here talk about it. If they know a Vegas area coaster, it's whatever they call Manhattan Express now. I agree about the Disney coasters, and would add Big Thunder Mountain Railroad, but I think the best known non-Disney coaster is Cyclone. Hulk and Dragon Challenge would be up there too. And RotM, I guess.
No one outside the coaster community or the UK knows Oblivion, Nemesis, Ultimate or the Big One. However people the world over have heard of Space Mountain & even Cyclone at Coney Island. Like others have said, people might not know that Space Mountain is a coaster but they've certainly heard of it & know it's at Disney. If you say "the Cyclone at Coney Island" to just about anyone, they know or guess that it's a roller coaster.
As far as Dueling Dragons, Hulk, Kingda Ka or Top Thrill Dragster - I don't think most people will know them by name or even exactly what they are.