I'll start with a couple where I think the original is best, and you guys can post some where you think the cover is better than the original:

This version (the original) by Ednaswap for me will always be much much better than the Natalie Imbruglia cover. It's a shame the cover was so much more popular because the original is miles better imo.
Natalie's cover
https://www.youtube.com/watch?v=VV1XWJN3nJo
Ednaswap original
https://www.youtube.com/watch?v=-7ULhmJIi4s
Also The Toyes original makes Sublime's version look like ****e compared to each other
https://www.youtube.com/watch?v=4UUPY902Ph0
https://www.youtube.com/watch?v=h0i62GnQoo0