No (mostly). 

This is unreal! First HD panorama of Mars! panoramas.dk/mars/greeley-h…

— Cory Morton (@corymorton) August 8, 2012

That picture certainly is an HD panorama of Mars. But it’s nowhere near being the first, and it wasn’t taken by the Curiosity rover which landed on the planet a few days ago. It was taken by the still-functioning Opportunity rover between December 2011 and May 2012 (you can find the original TIFF, with added data, on NASA’s site). If you look at the home page of the site it’s on, they have HD panoramas from the MER mission (which comprised the twin rovers Opportunity and Spirit) dating back to January 2004. And the first panorama from Mars was actually taken by Viking 1 back in 1976.

Curiosity has sent back a panorama of its location, but it looks like this:

UPDATE: NASA have just released Curiosity’s first colour panorama.

And the picture of “sunrise on Mars” being attributed to Curiosity is also not actually taken by Curiosity:

No need for photographic competitions this year. NASA has already won with: Sunrise on Mars. #Curiosity #Breathtaking twitter.com/skydavidblevin…

— David Blevins (@skydavidblevins) August 9, 2012

It was taken by the Spirit rover in 2005. And it’s of sunset, not sunrise. It is on Mars, though.

There’s no shortage of genuinely stunning images coming out of the Curiosity mission, however (there’s even a GIF!) so not every picture ascribed to Curiosity is necessarily misattributed…

UPDATE: Another Martian picture that’s been doing the rounds, also attributed in many places to Curiosity, is this one:

Earth seen from Mars last Saturday twitter.com/Newstalkfm/sta…

— Newstalk 106-108 fm (@Newstalkfm) August 19, 2012

Unlike the others, this isn’t just misattributed to the wrong rover - it’s not a genuine picture from Mars at all. Phil Plait at Bad Astronomy has a convincing debunking of the image, which he suggests is most likely a rendering from a piece of astronomy software.