I think the problem is that it is a fairly easy song for a band to perform, but for some reason very difficult to sing correctly. The most common problem is for the singer to forget the song is about a stalker girlfriend, and the delivery needs to tell that story. A ton of singers deliver it like it's some kind of up-beat lovey pop song, and that completely ruins it.
Also I don't understand the urge to over vocalize the song. It seems best sung in a subtle, narrow range with jazzy voice. Growls should be used sparingly.
Here's Blondie live for reference:
1. Kate Nash. Arguably better than the original if you like the modern jazzy vocal style. Shorter song though. I didn't care for the band so much.
2. Rock Legs. Quirky band from Brazil. Not the greatest vocals but solid delivery of theme. Hard to tell if the delivery was intentional or just coincidence, but either way it works. As a side note, the band handles the fast tempo very well...many bands fell apart on this song with a fast tempo. Solid base line that helps drive the song too.
3. Sunday Girl. This tribute band deserves an A for effort. Amazing how it could be so much better than hundreds of other covers just by doing the basics of the song correctly!
If you don't think these are that great, trust me--browse youtube for yourself and suddenly these will seem pretty good. Send me any gems you find!