Himself!
I seem to remember hearing that Van Hagar’s Finish What ya Started was recorded in one take, but I could be wrong… it’s happened before, so I’ve been told. 
S^G
I heard Roy Orbison once say that he did most of his early recordings with the band in complete song takes. They might record more than once and pick the best, but they didn’t edit pices together or overdub.
I may be mis-remembering but I think the outro on “Can’t You Hear Me Knockin’” by the Rolling Stones was just an unplanned, improvised jam led by Mick Taylor that was left on because it was so cool.
Well, they weren’t big hits, but damn near everything the Minutemen recorded was done in one take, live, direct to 2-track.
<sniff> We still miss you D.!
The Eagles’, “Heartache Tonight” was supposedly recorded all “live” in the studio – harmony vocals, guitar solos, the whole thing, straight up, no additions after. I don’t know if they needed more than one run at it, though.
That famous recording artist Robert Mitchum did “Thunder Road” in a single take and it became a very big hit.
Maybe not modern enough, but wasn’t Springsteen’s Nebraska pretty much just the demo tape he recorded in a hotel room?
That was standard practice in the early days of recording, and didn’t really end until the mid-60s. There might be multiple takes of a song, but everyone played at once and the final version would be the best.
The Grateful Dead album “In The Dark” was recorded as a live in the studio album by the band, and was actually performed, get this, in the dark. There were no lights in the studio so that they payed even more attention to the aural nuances of the music. This album of course spawned the Dead’s only hit single “Touch of Grey”.
Someone in Elton John’s band, speaking in the Two Rooms documentary, said that he does everything in one take. However, the band and guest vocalists (like the Beach Boys on “Don’t Let The Sun Go Down On Me”) usually do multiple takes.
Just to be a pill (and because you stole my choice), I’ll mention that the name of the album is “The Trinity Session” (no ‘s’) for exactly that reason.
ZZ Top’s first album.
Not necessarily a hit, but La Villa Strangiato, a very complex sounding 10 minute Rush instrumental was recorded in one take. According to Geddy Lee, it took them 40 takes to get it right. That’s dedication to a concept.
Perhaps the greatest guitar solo ever; Maggot Brain by Eddie Hazel/Funkadelic. Story goes that George Clinton told him to “play like your Momma just died”.
So then it was 40 takes, you can’t just count the one where they got it right otherwise most music before the advent of heavy studio equiptment and multi-track recording got all of their songs in one take…eventually.
Maybe a distinction should be made between:
- Recording a song “live” in the studio – no later overdubs, no fixups, no nothin’, straight to disk, and
- Recording the song in one take (which would encompass definition 1).
I mean, jeez, I’d think the band would get to the studio, tune up, check the levels, then rehearse the song a few times. Then nod to the engineer to start recording (“one, two, a one two three!”). Is that one “take” ? They just played the song more than once, but only had the tape rolling the final time.
A “take” is the first time that the recording information is turned on. Rehersals and warm ups don’t count, but when you’re taking up tape, you’re taking. If you do it 10 times while the tape is rolling before you nail it, then that’s 10 takes. If you did it just walking in off the street, picking up the instruments, nodding to the engineer and blowing it away then you did it in one take “cold” which is even more impressive but in the annals of rock history that kind of thing is mostly reserved for guitar solos. I’ve not heard too many storys of too many bands who could pull that off without just even a little warming up.
Fair enough, and that’s the way I’d define it as well, but there seems to be some confusion here about what the OP means.
I’d add that recording a reasonably complex song “live”, in any number of takes, with no later overdubs for vocals or solos, is pretty cool as well.
Not sure if it counts but Oingo Boingo made a 2 disc set, sort of a “best of” called Boingo Alive, where they rerecorded their older songs in one take “live” performances in a studio.