Hm, not good at predictions, but here goes.
The Supreme Court will continue to pass rulings that limit civil rights and increase the stranglehold corporations have on the United States. Barring an attack of conscience on either Roberts’ or Kennedy’s parts, the Court will find a way to duck settling the gay marriage issue.
There will continue to be gridlock in Congress, but thanks to the Democrats and Obama’s innate inability to stick with their demands, we’ll see austerity implemented and entrenched, with a negative impact at some level for nearly everyone in the country.
Obama’s healthcare law will continue to be whittled away at, although we won’t really see what happens until 2014.
As @johnpowell notes, we will probably have another spate of mass shootings, accompanied by the usual hand-wringing about how we need to finally do something about it. The furor, as usual, will die down after a couple weeks. Wash, rinse, and repeat.
Globally, there will be continued weather events that are far more intense/destructive than in past decades, leading to an increasingly stronger consensus that not only is climate change real, but we’re in the midst of it; but there will continue to be no real action on the parts of governments/nations/regions to even begin to mitigate the damage we’ve done.
Syria’s government will fall at some point during the year, but no one will be really satisfied with their replacements or the outcome.
Greece will exit the EU, which could lead to serious changes in the EU or its dissolution (or the beginnings of steps towards dissolving).