Some of my favourite covers off the top of my head:

It's My Life - No Doubt (TalkTalk)
A Little Respect - Wheatus (Erasure)
It's Not Over Yet - The Klaxons (Gloria)
You've Got The Love - Florence & The Machine (The Source/Candi Staton)
My Hero - Paramore (Foo Fighters)
Use Somebody - Paramore (Kings of Leon)
Hallelujah - Jeff Buckley (Leonard Cohen)
Hounds of Love - The Futureheads (Kate Bush)