Most larger video game series produce rearranged versions of fan favourite tracks from a particular video game, which in many cases can be better than the original song itself! So what are your favourite rearranged versions from any game? It doesn't necessarily have to be an official rearrangement: many Youtubers love to cover video game songs.
Here are some of mine. The Persona people love to rearrange songs, especially from Persona 3 and Persona 4, for anime, concerts and what have you. Called Reincarnation, the album rearrangement for 'Like a Dream Come True' is a fantastic jazz arrangement of the original from P4, as is 'specialist'.
Suffice to say, many of the Reincarnation songs made their way into Persona 4: Dancing All Night.
Final Fantasy has had so many rearrangements, albums, concerts, that it's impossible to really narrow down one song. The Piano Collections are probably my favourite series of arrangements; I'm pretty sure every game has one.
Phoenix Wright is also a series with a large fanbase, and so has received a few arranged albums. There's a Jazz one, and an Orchestra one. Both are excellent.
But really, I find the different takes on classic songs can really improve them.
