Vita has a number of non-gaming apps, with many resembling apps you'd find on a phone. However, the Vita also has a few quintessentially Japanese apps--and surprisingly, they are coming to the US as well.
Perhaps the most novel app coming to Vita is "Wake-Up Club." Available this summer, it turns your Vita into an alarm clock. Sure, that sounds helpful--but it also includes a multiplayer feature.
Setting your alarm for a time that other Vita owners must also wake up will enable a multiplayer mode. Perhaps your on-time waking performance will contribute to some PSN trophies? That should provide added motivation to wake up on time, right?
Paint Park is yet another free app for Vita, coming April 18th (that's tomorrow!). Essentially Microsoft Paint for Vita, the app will also let you take photos with the camera and edit them by carefully drawing mustaches on the subjects. Unfortunately, this is not a Vita port of Draw Something.
Finally, the last free app announced by Sony is Treasure Park. This app lets you create your own puzzles and share them via Near. Treasure Park is also coming in the "summer."