It is mostly used in subtitles and in the credits. Here the example:
From the answer to this question there are some sites with recreations of the fonts used in Pokemon games.
The actual font is most likely a custom font created for the game and not available elsewhere.
I think the one closest to the one you're looking for would be the Pokemon Mystery Dungeon or Pokemon Diamond and Pearl fonts in the second link.
It is the regular form of "Rodin" from Fontworks. New Rodin's latin characters are what I could call "square sans," but if you look closely, the letter "e" in Rodin has a straight bar that is off angle. The straight part before you curve the "e" isn't perfectly horizontal; it's slightly tilted counter-clockwise so that it's a bit upward than usual. Anyway, that's how Rodin is usually identified—by the lower case "e."
Because of the better screens in the 3DS, it seems like higher quality fonts and better graphics are being used in place of the lower quality fonts and graphics used in pre-3DS games.