Dissidia Duodecim is easily my favorite Final Fantasy title. The idea of putting a bunch of characters from different games or universes into a single game has been done time and again, but Dissidia handles this fantastically well. Not only does Dissidia manage to be the most varied Fighting game series that I've ever played, as well as being the most innovative 360 degree Fighting game I've played in years (and the fighting game that Dragon Ball Z should be- well, at least the Tenkaichi series), but it also manages to create a very tight and compelling narrative that pulls the player in regardless of whether they've played mainline Final Fantasy games or not.
Even more on this, it takes characters who previously had little, weak, or in some cases obnoxious personalities (either out of intention or otherwise), such as the Cloud of Darkness, Vaan, and Tidus, and making them into stronger characters, even if they don't have very much story presence or, in their respective original games, didn't have their own personalities because they weren't technically actual characters (this being the case with the Warrior of Light and the Onion Knight). The story's premise is simple, but it finds most of its attraction value in making it a character's game, largely about what they fight for and putting their dreams and motives (or lack thereof) headfirst, largely being the cause of most of the story's growth and development. It's really interesting, for a Final Fantasy game such as this to feature the amount of character development that it does, both on the level of forming relationships with other characters and in finding themselves. The game also does a great job of making the interactions between the surprisingly human antagonists and the protagonists both tension filled and contrarily casual, largely due to the nature of the premise.
I never had a PSP before, so it wasn't until early this year that I got to buy it on my Vita, and I definitely recommend it to any Final Fantasy fan or...pretty much anyone that has a PSP/PSV/PPSSPP.