I got the impression they’ve made peace with it in recent years, but they certainly grew to hate the song after it was a hit.
I was working concert security in college and a country band, Little Texas, I think (I don’t do country), was playing. I was in charge of watching the dressing room, and they apparently had a big hit song around that time (1994-95). As the band was coming down to the dressing room after closing the show with their hit, one of them said, “God damn. Who wrote that piece of shit? I swear, I hate that song more each time we play it.”
I think that would count as an artist regretting making a song.
I heard the singer from Warrant say he regrets writing “Cherry Pie”, he felt it defined the bands sound in the public’s mind in a unflattering way.
As he should!
I should read the other posts first!
The quote appears to be several years old, however; don’t know if Stipe’s feelings have changed since. But it doesn’t seem as if “regret” is an appropriate description.
Along similar lines, both Warren Zevon and Randy Newman expressed regret about their most successful records (“Werewolves of London” and “Short People” respectively) because they made the general public think all they did were “Purple People Eater”-type novelty songs.
Greg Kihn of the Greg Kihn Band is the morning DJ on a local radio station. He still does the occasional concert. One morning he was bemoaning the long high note in one of his most popular songs. I’m not sure if he regretted the song altogether, or just regretted that singing high notes was getting harder and harder as the years went by.
I also heard that he can not be hired to perform just that song. He will only play it if he is hired to play an entire set list of his music.
I’ve heard Billy Joel say the same thing. It’s not that he regrets writing the songs, but he would have written them differently had he taken into account that in 20 years he wouln’t be able to hit those notes any more.
There’s a “history of rock” documentatry type show on a radio station here (it’s actually really cool because you hear great music but the show is set up with lots of info like a well researched article). Anyway, one segment talked about some one hit wonders and had a factoid about Paul Young (not the Mike + the Mchanics guy, the No Parlez guy from the 1980s). In the 1970s, he was in a band called Streetband that was trying to find a voice as a new wave group, but as a joke they recorded a goofy tune called “Toast”.
In some interview he said he regretted ever releasing it. It was not at all representative of the sound of the band, but because it was a one-hit wonder that’s what everyone came to hear. He said their gigs turned to shit because totally the wrong crowd started coming and were disappointed. So their one “hit” effectively killed the band.
Just like most people these days know Todd Rundgren for “Bang On The Drum All Day” and “Hello It’s Me”. He got his revenge on the latter song by re-recording it on his Bossa Nova cover album “With A Twist” as a creepy stalker. “Bang On The Drum” he sold outright to a marketing company that has managed to place it in movies, commercials and sports venues.
Springsteen has said he regrets the way that Born in the USA is arranged, in that by making it sound upbeat and anthemic, he pretty much invited the widespread misinterpretation of the song.
It’s probably as solid a concert staple as he’s had for the last 15 years – but always a completely different arrangement, that brings out the darkness in the song.
The legendary Vanilla Ice grew to hate “Ice Ice Baby” so much that he destroyed MTV’s tape of it during some MTV interview show, and then proceeded to destroy some other stuff on the set as well.
I’ve also read that Rundgren also hated “I Saw The Light” (“a string of meaningless cliches,” I think he called it).
In a somewhat different er… style, I heard Tchaikovsky grew to hate one of his Symphonies (I think it was one of them in C-something, I don’t recall though) because everyone always wanted him to play it. He got to the point (or so i’m told) that he referred to the song as “it”.
Great White won’t play Desert Moon anymore. But it’s not really because of the song but the events surrounding it’s last performance.
I’m not sure that David Bowie is all that keen on the “Laughing Gnome”. 
I don’t know if they actually regretted it, but Aqua has expressed dissatisfaction at being the “Barbie band”, at least outside of Western Europe.
Valete,
Vox Imperatoris
The Cure added a sticker on the CD “Staring at the Sea” decrying the use of “Killing an Arab” as an Pro-Iraq war anthem.