This. Although I'm inclined to say Noel Gallagher's High Flying Birds at the moment. He said himself that it's ambiguous as to whether it's a band/solo act but for the sake of this thread I'll consider it a band!
Current: Stereophonics, I love Kelly Jones' voice and the songs have some awesome melodies and the lyrics are lush!
Broken up: Oasis, you literally cannot beat Oasis!
From the past: The Beatles (obviously) and The Kinks!