What openings typify 21st century chess? What openings are particularly typical of 21st century chess so far?  To be more clear, which openings are particularly popular in the 21st century relative to the 20th century?  For example, certain hypermodern defenses became a lot more popular in the latter half of the 20th century relative to the first half of the 20th century.
Here are a few openings that seem to be played more often in the last decade than previously.  This is just based on my recollection, so please correct any errors or add any other openings.


Catalan Opening
The last few major matches have all featured the Catalan: Anand-Topalov, as well as the candidates matches leading up to the World Championship 2012. The Grandmaster Repertoire by Boris Avrukh has also contributed to the recent popularity.
Berlin Wall
Kramnik brought this opening to the forefront when he used it with devastating effect against Kasparov.  The queen-less middlegame has been deeply studied since the match in 2000.  This line is partially responsible for the rise of 1. d4 and the fall of 1. e4 in the last decade.
Grünfeld Defense
While the Grünfeld was played fairly consistently throughout the 20th century, only recently has it become the main weapon for black when playing for a win against 1. d4.  The Grünfeld doesn't surrender the center like the King's Indian Defense, and it has become more popular the more it is studied, as opposed to the Nimzo-Indian which has fallen by the wayside as the Qc2 lines have been examined.  


Other openings that have been featured in high level games have been the Slav Defense and, as always, the Sicilian.  I omitted these openings because, while new lines are always being developed, these openings have been popular consistently for a long time.  

Additionally, as I mentioned in my comment, some gambits have also seen a revival.  The Morra Gambit, for instance, has come back to high level play and several books about it have been written.  The Evan's Gambit is another opening played at all levels.