The Bobby Fuller Four's hit version of I Fought The Law is considerably better than the original by the Crickets, but the later cover by the Clash is better still.

Siouxsie & the Banshees' version of Dear Prudence is much better than the Beatles' original. Their version of Helter Skelter is also superior (in my opinion at least....).

I prefer Blancmange's cover of Abba's the Day Before You Came, but they're both great.

Bowie's version of China Girl is a good deal better than Iggy's original.

The Damned's cover of Eloise is better than Barry Ryan's original, although that's also quite decent.

The Pretenders' cover of I Go To Sleep is better than the Applejacks recording or the Kinks original (but that was just a demo).