Tyler Cowen has a post about What is emblematic of the 21st century.
It's a pretty sensible list for the most part. Probably the most obvious answer is the rise of information technology/social networking: smartphones, youtube, google, facebook, twitter, blogging, etc. The internet was already important in the 1990s, but think about the fact that people can now do a day's work from an IPad. I would add to this the rise of online universities and telecommuting. Also, taking into account online grocery shopping and ebay, the 21st century is probably the best time ever to be a recluse.
Another interesting trend is the increasing unsexed-ness of our society. I mean this in the Lady Macbeth sense, rather than the Steve Carell sense. The idea that the differences between the sexes are trivial has become more widespread. Some radicals asserted this in the 60s and 70s, and there was something of a push back in some ways. However, the idea stayed alive, and by 2010 this idea of a sexless society has become almost taken for granted by large swathes of the population. Maybe in a few crazy Red States, the sex differences live on. But in the land of yuppies that I live in, the idea that one's sex has anything to do with one career choice or roles within a family seems rather archaic. An example is how uncontroversial gay adoption is now. I imagine the idea was considered radical even 20 years ago. The sex-based division of labor appears to have been a central facet of human existence ever since the species began. It'll be interesting to see what happens if and when this arrangement dies.
Something could perhaps also be said about the rise of "smart", irreverent, no-holds-barred humor of the sort found in Arrested Development, The Office, 30 Rock, Judd Apatow movies, South Park, Curb Your Enthusiasm, etc. (Maybe this isn't so different from SNL, which goes back to the 1970s, or Seinfeld.) I don't know of a smart way to analyze, so I'll leave it to someone else.
I also wonder what the big religious stories of the century will be, other than the rise of the "Global South." Maybe the thawing of China?