To continue my discussion of videogame music...
I am rather fond of having theme music for the important characters in a game. The more important the character, the more important it is for them to have theme music. I suppose this is simple enough, but there are a few places which do interesting things with the concept.
First, I think Wild Arms 5's use of character theme music, particularly Avril's main theme, is an example of how effective character theme music can be. In this game, Avril is pretty much the central character of the plot, and one of the most complex and fascinating characters in the game, Her theme music, a beautiful and haunting melody, matches her quiet, dignified, and mysterious character very well. The interesting element about her theme is that the main melody from her theme appears in many different songs, for many different purposes. The boss-battle variation of her theme is great, and the variation from a dramatic point in the ending, which has been altered heavily in tone and energy, is very fitting for that desperate, hopeful, and bittersweet sequence. Because her theme reappears in many forms to fit the tone of the story, and is powerful and memorable, it adds a lot to the game.
Wild Arms 2 has a minor use of character theme music which is rather fun. In this game, whenever the main hero Ashley uses his Access ability to transform into his powerful Knightblazer form, the battle music changes to Knightblazer's theme. It makes the transformation ability feel more special than other character abilities, and makes the use of Knightblazer more exciting.
Another interesting approach to character theme music is the various songs from the Super Robot Taisen series of tactical RPGs. In this series, the music changes to a character's theme song every time that character attacks an enemy or gets attacked. As a result, you are likely to hear something like 20 different character themes every turn in a battle. This use of music is a product of the series' role as a giant crossover between various anime mecha series, and is designed to make use of the nostalgia and popularity of well-known songs, but it works very well even for the Original Generations iterations of that series, which are not based on television properties and do not have as much nostalgia value. This use of music does a lot to help distinguish characters, and complements the flashy style of the elaborate attack animations and colorful mecha designs. Part of the reason it works is the way the attack animations play out separate from the main battlefield, focusing the player's attention on a single character. In other tactical RPGs, like the Final Fantasy tactics, where individual attacks are subdued and take place in the main battle map, this use of music would probably not work as well.