The Bad Lip Sync version of Gotye (Kicked Your Monkey And I Used Your Goat) kinda always comes to mind

Maybe a stretch as it’s not parodying a song but parodies Star Wars kinda sorta? Seagulls! (Stop it Now)

Lonely Island has a few (Jack Sparrow) comes to mind but again not a direct parody of a specific song.

Richard Cheese does straight up covers but they are so stylistically different that it’s basically a parody. Chop Suey

Then there’s the classic comedy music duos: Garfunkel & Oates (Loophole), Flight of the Conchords (Business Time)

Bo Burnham’s whole Inside special is fantastic too.

Looks like I’m mostly listing comedy music and not necessarily parodies, but oh well.

United breaks guitars.

Not quite parody but…

I had a friend who sung I Can’t Feel my Face when I’m with you, as I can’t feel my face when I Go POOP and that is all I will ever hear now.

Nanobot by A Capella Science. The whole channel is pretty good, but this song just shines above the pack. Shivers every time:

https://www.youtube.com/watch?v=ObvxPSQNMGc

Love is A Battlefield literal video is hilarious to me.

https://youtu.be/ca2aSzu_2iA

Bo Burnham’s Kanye Rant

https://youtu.be/rYy0o-J0x20