My favorite and most controversial picks:
Save Ferris - Come On Eileen (originally by Dexy's Midnight Runners)
I'm not much of a ska fan, but Save Ferris's version of Come On Eileen has so much more excitement and energy than the original. I love how hard the guitar sounds as it leads into the chorus. The lead vocalist was originally trained in opera, and consequently she has a lot more range and emotion than the singer in the original version. The final breakdown that occurs around 3:15 makes the song's ending feel much bigger and more climactic.
No Doubt - It's My Life (originally by Talk Talk)
Another ska band.....huh. As with Save Ferris, I think Gwen Stefani does a much better job on lead vocals. I think having real instruments works better than the synthesizer-heavy original version. I also think the video is pretty incredible -- it was directed by notable photographer David LaChapelle, and it is dripping with his glam style. I love that it was made while the band was on the verge of breaking up, and features Gwen Stefani killing off all of her fellow bandmates just before she embarked on a solo career. I always have to wonder exactly what the mood was on that set!