Like the Sony PSP, the new PS Vita can be hacked provided you have the tools and knowhow to do so. The hacked system can be made to run various games on an emulator, along with a host of other homebrew software. Case in point, some users at wololo.net have figured out a way to get Doom running on the PS Vita with the 1.67 update.
In an attempt to address these vulnerabilities, Sony pulled two games (via Joystiq) from the PlayStation Network in March. The two games, Hot Shots Tennis and Motorstorm Arctic Rift for the PSP allowed players to use homebrew programming through the system's PSP emulator. Despite the company's move to clamp down on homebrew software however, hacking the system is still possible, as evidenced by the video above.
Before you decide to get a Vita for the sole purpose of running emulated games, know that doing so is against the company's official policy and that they're doing their best to stop people from doing it.