I've always felt covering a popular song and making it not only good but also your own song is one of the most difficult things in music. Mainly because everyone is always going to be comparing it to the original. And the more iconic the original song the more difficult to make a cover of it and have it anywhere near as good as the original.
Make it too much like the original and you're playing it safe to the point of boredom but veer too far away from the original intention of the song and you risk losing your audience completely or even angering them. It's a fine line but some manage to do it very well.
I thought I would post a few covers and mash ups that I think manage to walk this line. If you are inclined please post some as well.
Heres one that is quite far from the original version of the song but is considered by many to be a great success as a cover.- Mad World - Gary Jules, cover of Tears for Fears.
https://youtu.be/Oa-ae6_okmg