I ain't really a fan of the anime music, but the Battle Frontier theme was one of the best, second to the original theme.
As for the games...
For Generation I, my favorite battle theme is either the Gym Leader or Champion theme, and my most favorite area (I'll just call it that) is Cerulean Cit or Surfing. I ain't a fan of FRLG's music, however, because it was a little high-pitched compared to the original.
For Generation II, my favorite battle theme is either the Champion or Legendary Beast theme, especially in HGSS. For the area music, either Goldenrod City, Tin Tower, or Route 38. In HGSS, Route 47 also ties with them.
For Generation III, I slightly dislike FRLG's music (except Route 1, Sevii Islands 1 and 2, the Gym Leader battle theme, and Surf), though I have a lot of faves in RSE, particularly the Elite Four and Frontier Brain theme, especially in the remakes. For the areas, Route 113, Route 119, Mt. Chimney, Victory Road, Ever Grande City, Route 120, Mt. Pyre, Slateport City, Sootopolis City, and Littleroot Town have to be favorites of mine.
Generation IV was all...jazzy. I'm not really a fan of Sinnoh's battle themes, but the Team Galactic battle theme was a great one. Also, my favorite area themes are Sunyshore City, Route 109, and Route 225.
Generation V had most of my favorites. There's a favorite war going on between the battle themes of the Elite Four, Iris, Hugh, wild Pokémon (plus surprise attacks), trainers, the VGC, and Colress. For the rest of the BGM, Route 10, Accumula Town, Bicycle, Victory Road, and Dragonspiral Tower are my favorites.
Generation VI didn't introduce a lot of my favorite music, but the battle themes I prefer are Team Flare's, Xerneas, Yveltal and Zygarde's, VGC's, and the Elite Four's. As for the rest of the BGM, Anistar City, Cycling, and Super Training are sure favorites. I probably haven't liked them as much as I do the others because I have never played XY.
In terms of music, HGSS, ORAS, and B2W2 were the best. HGSS had that Japanese feel to it, ORAS was an orchestra, and I don't really mind the lack of French horns, and I certainly can't get enough of B2W2's techno style.