What Are You Doing…
…The Rest of Your Life?
Nope
Molesting My Wife
This one, for me, too. It’s one of my favorite Weird Al songs. 
O Sole Mio = Just One Cornetto
Anvil Chorus = Raguleto Pasta Sauce
Hah - yes indeed.
In 1985, we did a cross-country driving trip.
Whenever we could get radio reception (and there were quite a few places where we could not), it seemed everyone was playing Like A Virgin.
On the last few days of the trip, we tuned into a station and heard the last few seconds of it. We were delighted, thinking that it would be a while before we heard it again.
To our horror, it began playing again IMMEDIATELY.
Fortunately for us, we very quickly realized we were hearing the parody. I’ve been a Weird Al fan ever since.
Supposedly Madonna actually suggested the title for the parody.
Homer and Jethro’s parody of Johnny Horton’s “The Battle of New Orleans”:
On Top of Old Smoky/On Top of Spaghetti
Almost six minutes of Allan Sherman parodies here (some references are a bit dated)… Shticks of One and a Half Dozen of the Other - YouTube
It’s “one ton of metal” for me, like some scrap iron dealer.
I’m actually only barely aware of the original of that one. I had an album of parodies as a kid and On Top of Spaghetti was the best one, or at least the only one I remember.
I just looked up the lyrics to the original – I don’t think I ever heard it.
ETA: Here’s the album. Wow! Memories.
Oh, Gos, there’s so many of them.
It’s not just the Weird Al parodies and Alan Sherman and Peter Schickele/PDQ Back. There are also the parodies in MAD, mostly by Frank Jacobs, who just died a few months ago
I’m not sure if it’s one of his, but this one’s stuck in my mind:
(Side question – why is it that so many parodies, especially in Mad and by Al Yankovich, turn into songs about food?)
I can’t hear Jingle Bells without thinking of the Batman version.
Self-parodies by the original composers sometimes intrude on my memories of the real thing. John Lennon liked to goof around with Beatles lyrics (lots of examples in the Get Back six-hour film). And when I think of Paul McCartney’s “Yesterday,” I sometimes hear in my head “Scrambled eggs…oh, my baby, how I love your legs” — Paul’s own placeholder lyrics, before he came up with real ones.
Oh mg god, so this.
I was listening to a radio show in which they were talking about Lorde’s “Royals” a while back and thinking “This sounds really familiar and yet I’m sure I’ve never heard it before”. Finally realized that while I hadn’t heard it, I had already heard Weird’ Al’s version “You can wrap it in FOY-al…”
On the classical side, there’s an old joke about the opening solo in “The Rite of Spring” that the words to go with it are “Iiiiii’m not an English horn, Iiii’m not an EEEEENG-lish horn…”, which is amusing because it’s a bassoon playing in English horn range. I think of that every time. But that’s pretty esoteric.
Gonna echo many of the Weird Al posts so far and add that there were several years where I only knew most of the songs in “Polka Your Eyes Out” from Yankovic’s medley, so that’s the version I think of when I hear them.
This one from The Simpsons:
I can’t listen to Roger Whittaker’s “New World in the Morning” without singing my own creation “Good Dump in the Morning.”
About 20 years ago, I was doing some volunteer work at an Anglican church and for some reason started singing “How Do You Make a Movie 'Bout Religion?” from MAD Magazine’s satire of The Sound of Music. The Vicar was not amused! 
I Am Santa Claus to the tune of Iron Man.