What games can the Vita TV (PlayStation TV) play?

The selection of games the PSTV can play is determined by a whitelist, which means that instead of playing all games except explicitly disallowed ones, it plays no games except for explicitly approved ones.

As a general rule, the games that don't work are often dependent on Vita-only features, but this isn't true all the time. The PSTV does have the ability to simulate front and back touch inputs. There are also cases of games that can be played perfectly fine with button-only input not working, such as Hyperdimension Neptunia Re;Birth 1. There isn't always rhyme or reason to this, as the other games in the Neptunia series work fine on PSTV.

It's also worth noting that a game that doesn't work at first might become compatible later on due to software patches. Quite a few of my Vita titles that didn't work with my PSTV when it launched work fine with it now.

This whitelist doesn't only apply to Vita titles. There are also PSP, PS1 and PS Minis games known not to work.

Because whether or not a game works is subject to change due to patches, and also because a game may work in one region but not another, it is difficult to find all-inclusive and up-to-date lists online. This isn't helped by the fact that not a ton of people own this device.

If whether or not a title will work on PSTV is a major factor in deciding to purchase a game, one is much better off searching for an answer specific to that game, as the answer will often be found in forums.