K-On's actually an anime that focuses mostly on music. While there isn't much in the BGM, there are a lot of songs that are really vital to the plot, since it's about a high school band. The rest of the show mostly focuses on friendship and procrastination, but those parts have some of the most hilarious moments in the anime.
I can't say I've seen a lot of animes, but a brilliant one would be Puella Magi Madoka Magica. It starts off as your typical magical girl anime, with friendships and school and magic, which then gradually evolves into one of the most disturbing animated shows ever.
Also, the studio that made K-On had their new show, Tamako Market aired just a month ago. It's a hilarious one.