Erasure - Take A Chance On Me

Within Temptation's cover of Radioactive by They Might Be Dragons. Much better. That said, nothing can beat the hilarious acid trip that is the original's music video.

“(I can’t get no) Satisfaction” as covered by Cat Power. It completely omits the guitar riff and chorus, and lays bare the song for the empty life that it portrays. You wouldn’t even recognize it for The Rolling Stones.

Bruce Springsteen - Staying Alive

Megan McDuffee's dark synthwave cover of Blink 182's song Dammit

https://youtu.be/m-YYngv1mhM

Elbow's cover of Peter Gabriel's 'Mercy Street's MC 900 Ft Jesus' cover of Curtis Mayfield's 'Stare And Stare' Gypsy Kings' Spanish cover of Frank Sinatra's 'My Way'

A-ha's acoustic version of Take On Me is wonderful and very different from the original.

Baby I’m yours
Original by Barbara Lewis
Cover by Arctic Monkeys

Tool's cover of No Quarter by Led Zeppelin. Page was channeling future Adam Jones with those riffs. It's s a shame that the only official release of that song is on Tool's coveted "Salival" album which is notoriously hard to get ahold of for anything even resembling a decent price if you can even find a good copy. Damn, I wish they would re-release that album.

Eleanor Rigby by Pain

While I love the original version, Seethers cover of Careless Whisper is one of my favourite songs ever.

Kind of the opposite but "As the World Caves In". Most people know the cover by Sarah Cothran , but I think the original by Matt Maltese is way, way better.

It's a song about two people together at the end of the world, and while Sarah sings it mourning the loss of everything, Matt sings it as a love song. To me that's the much more powerful message, that when everything is burning down, the only thing that's left and all that really matters is being together with the person you love, and the only thing to mourn is that you won't have more time with them.

Gonna go retro with this one: Madness' cover of Labi Siffre's It Must Be Love

If I remember rightly, Siffre appears in Madness' music video for the song, so it had his seal of approval too. (I mean, yeah, they wouldn't have done a cover if he hadn't agreed to it, but appearing in the video is a force multiplier on that.)

I really enjoy this cover of Dead Man's Party

The Protomen's cover of Silent Running (On Dangerous Ground) is a slower burn than the original, but I feel like the emotions intented by the song are so much clearer.

It's off their album The Cover Up, which is an entire album of well done covers. It also tells a strong story through the tracks and the transistions between them. I love this band, and the last third of this album from Hunted (a transistion piece) onward is fucking amazing.

Now if only they could count to three better than Valve. Been at least a decade waiting for the ending of the story/universe they created. Act III when?

Ween's version of All of My Love. Which I've only ever heard through a crappy phone recording of a live event. Despite that, it's still better than the original.

The Z-Trip remix of I Want You Back, which is more of a demix than a remix or cover. It strips away a lot of the production and emphasizes the subtle guitar riff really nicely

https://youtu.be/zh-I31AsJJg

For as long as I've known it I've preferred the version of Ghost's Cerice done by Saint Raven, a much less known band out of Utah.

Heartbeats.

Original by The Knife,

cover by José González.

Same words, same melody, completely different universes.

Small town boy by Paradise Lost. https://open.spotify.com/track/0jfNgP8sP2tnOloYDw0HoM?context=spotify%3Aalbum%3A1lvVqodR4aT3R8WemeIgDN

The original is iconic, and there are almost too many covers of it to take it in. But Paradise Lost takes it in a different direction.

Same as Wicked Game by HIM. https://open.spotify.com/track/5XenUjG7cRnTkUe8AVuuMX

Love roller coaster covered by the Red Hot Chili Peppers, originally by the Ohio players I think, unsure because there’s been a few covers, but RHCPs is the best. The problem is they did it for the movie Bevis and Butthead do America, and I’m now there are weird license rights so you can’t stream it, but can be found on you tube.

This is the opposite of what you're asking for, sorry, but I find that more people are familiar with the A Perfect Circle version of The Nurse Who Loved Me than they are with the original version by Failure.

Both very good versions song, but the original still blows me away.

Apologies for doing the opposite of what you asked, but this was just the first thing that came to mind.

Electric Callboy - Every Time We Touch

Israel Kamakawiwo'ole - Somewhere Over The Rainbow

Shawn Colvin - I'll Be Back

Sonic Youth - Superstar (btw not originally by The Carpenters)

John Mayer's cover of Free Fallin by Tom Petty. The vocal, the sweet guitar. I love it.