A couple I got from my years as a Kiss fanatic:
Buckcherry’s song “Lit Up” has basically the same guitar part as Kiss’ “Shock Me” from *Love Gun *or *Alive II *(but please, for the love of Og, stay away from any version you might hear with Tommy Thayer singing lead).
Kiss borrowed a little from Jimi Hendrix’s “Foxy Lady” for “She.” Eric Singer (current and former Kiss drummer) and Bruce Kulick (former Kiss guitarist, now with Grand Funk) were briefly part of a project called ESP (Eric Singer Project) and made an album with a cover of “Foxy Lady” in which they made the similarities obvious enough for almost anyone to catch.
ETA: Yeah, can’t access YouTube from here, or I’d post links… not that I think most people are that interested in Kiss.
k.d. lang - Constant Craving
vs.
Rolling Stones - Anybody Seen My Baby
Some of these are admittedly more in the “spookily similar riff” vein rather than being basically the same song. There were more examples in that programme such as the aforementioned Killing Joke/Nirvana one. I’ll see if I can dig out the recording.
Opening parts of DeGarmo & Key’s “Rebel for God” and Whitecross’ “When the Walls Tumble” are pretty identical, but I wouldn’t expect you to know either song unless you’re into 80s Christian metal …
Obvious to the point that George Harrison was sued for copyright infringement and lost. I believe he ultimately conceded the similarity but said that it was not an intentional imitation.
The opening of the Indigo Girls’ “Tried to Be True” always reminded me of The Who’s “Don’t Let Go the Coat”. I used to listen to a radio station that had both songs on its playlist, and it often took me a few seconds to figure out which one I was hearing.
Part of Leonard Cohen’s oft-covered “Hallelujah” sounds like Elvis’s “Can’t Help Falling in Love” to me. Wikipedia tells me that the melody of “Can’t Help Falling in Love” was borrowed from the French classical song “Plaisir d’Amour”, so it actually predates Elvis by more than a century.
A couple of years ago there was some new song that I always thought was a cover of a Rolling Stones song until the lyrics kicked in, but I’m afraid I can’t remember what the two songs were. :o
I learned from Pop-Up Video that the Stones noticed the resemblance before the song was released, and hastily added lang to the songwriting credits (thus granting her a slice of the royalties) to head off any potential lawsuit. lang reportedly said she was very flattered to have been considered an influence.