This one is also by NeoMikey, and the music is U2's Beautiful Day, performed by the Christian band, Sanctus Real. The video is from FLCL, quite possibly the weirdest, most engaging, most FUN anime ever produced. The series is six episodes of the prodution teams' imaginations set loose. The song really fits the show to a "T". Oh, pay attention to the characters' mouth toward the end, when the line "I know I'm not a hopeless case" starts. Somehow, he got thier mouths to sync with the lyrics, and it's freakin AWESOME! Anyway, ENJOY! It's FUN!
Edit: There's even more lip-synching than I thought. The first line of the song, pretty much every "Don't let it get away", and a few others are synched as well. Pretty slick.