As a big fan of both the Ramones and Tom Waits I'd be remiss not to include the following on my list of good covers...

The Return of Jackie & Judy - Tom Waits (originally by the Ramones)
Danny Says - Tom Waits (originally by the Ramones)

Tom is a master at arranging songs. To be honest, I've always thought "Danny Says" was a good song lyrically but never really cared for the original arrangement which I thought was overproduced (not unusual since that album was produced by Phil Spector who has a very heavy hand in the studio). Tom's version shows off what a great song it really can be when it's stripped down.

And on the other side of the equation...

I Don't Wanna Grow Up - Ramones (originally by Tom Waits)

They're version of this song is fairly straightforward - they weren't exactly virtuoso musicians so I don't expect them to come up with unique arrangements, but there are many covers which got the Ramones treatment which don't always come off so great. This one sounds perfect. It's also notable as one of a very small number of songs on which Johnny plays a solo (albeit a brief restatement of the melody).