Coders have managed break the protection on the PS Vita using an exploit called HENkaku. The exploit allows you to install software that's not been approved by Sony, including emulators. It also lets players whitelist all the games on the system, letting them load games locked by Sony. It's even letting developers overclock the console.
It's extremely easy to make use of the exploit. A group called Team Molecule has created a website that you can visit from your Vita that lets you download code that then lets you send files to your Vita using an FTP server.
The creators say that "[i]t does not let you install or run Vita “backups”, warez, or any pirated content. It does not disable any DRM features. It does not let you decrypt encrypted games. Here’s my stance on this: I do not care one way or the other about piracy. I do not judge people who do pirate. I will not act as the police for pirates. However, I will personally not write any tools that aid in piracy. It is my choice just as it is the pirate’s choice to steal content."
However, with the ability to install emulators that can run ROMs, this is a way to have your Vita play games that weren't built to run on the handheld. There are already versions of Quake and Doom that you can get onto the Vita thanks to HENkaku. There are also emulators for the SNES, Sega Genesis, Game Boy and Game Boy Advance if you go looking.
The exploit only works if you have the the 3.60 firmware installed on the Vita and if Sony releases new firmware it may well prevent this new exploit from working.
And, of course, sending code packets to your handheld opens you up to installing malicious code on your device. So, if you are thinking of using HENkaku, be aware of that.