Mostly songs from the sixties come to mind, as songs where the performers came in, laid in down in one go and left.  No fumbling around in the studio for days on end, just in and out.

Two of I know off the top of my head:

Kingsmen, "Louie, Louie"
Dave Clark Five, "Bits & Pieces"

The Clash, "Rock The Casbah" was mostly laid down in one take, one track at a time by it's author as well.

The Beatles' song "Twist and Shout" was recorded in two takes, but the second take was discarded.

Isn't it said that Celine Dion's "My Heart Will Go On" from Titanic was a one take version. I thought it was laid down as a demo to play for whats-his-name the director of the film, the director heard it then he let it in.

Apparently, Dione Warwick nailed the cover version of the song 'Alfie' in one take. This was a remarkable feat as the British singer, Cilla Black, who had a world wide hit with that same song described her recording experience with Burt Bacharach (for that song) as the most demanding of her career.

But Dione was the greatest interpreter of BB's music...

The 1979 cover of 'Money (That's What I Want)' by The Flying Lizards was apparently recorded in one take.  It was also said to have been recorded a dark basement, rather than a recording studio.

It failed to become a Top 40 hit in America, but was a Top 5 hit in the UK and a Top 10 hit in Canada and is the most widely used version of this song.

I vaguely remember reading somewhere that Roberta Flack recorded all the songs on her first album "First Take" in just one take ??

http://en.wikipedia.org/wiki/You_Keep_Me_Hangin%27_On

Vanilla Fudge's 6+ minute version of "You Keep Me Hangin' On" is a one take song

Chamber Brothers, "Time" the version we all know and love is a one-take song too..

The Beatles' song "Twist and Shout" was recorded in two takes, but the second take was discarded.


Their version of the Chuck Berry chestnut 'Rock And Roll Music' was nailed in one...

Bill Haley's 'Rock Around The Clock' was almost recorded as an afterthought...two takes were recorded, but the final master is an edit of those two takes, so technically, it could be in with a 'one-take' consideration...

I believe that Billy Swan's I Can Help was recorded in one take, and because it sounded so good, a reprise of the song kicks of after the cheering, which is heard on the end of the recording.

learned of a new one today on a reddit thread:

Neutral Milk Hotel's "Oh Comely" is a little over 8 minutes long and Jeff Mangum reportedly recorded the entire song in one take, which is very impressive, so impressive that at the end of the song you can barely hear someone say "Holy sheesh!" at the end of the track in the background

Wannabe by Spice Girls was done all in one shot.  :)

And basically, ANY recorded song issued prior to 1948-ish would be a one-taker, as recording studios hadn't had tape recorders installed (thank Bing Crosby for this!)

If someone fouled up - new lacquer disc and from the top...

Wannabe by Spice Girls was done all in one shot.  :)
The video by the director Jhoan Camitz was done in one take, but from Wiki:

"While most of the other songs on the Spice album required two or three days of studio time, "Wannabe" was recorded in under an hour. The solo parts were divided between Brown, Bunton, Chisholm, and Halliwell. Beckham missed most of the writing session and communicated with the rest of the group on a mobile phone. In her autobiography Beckham wrote: "I just couldn't bear not being there. Because whatever they said about how it didn't matter, it did matter. Saying 'Yes, I like that' or 'Not sure about that' down the phone is not the same". She contributed backing vocals and sings during the chorus. Rowe stayed up all night working on the song, and it was finished by morning."

The song not done in one take.

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Someone mentioned that Mark Holmes was coughing 03:07 indicating that they must have done this song in one take. 

found a new one today

https://en.wikipedia.org/wiki/In-A-Gadda-Da-Vida

The recording that is heard on the album was meant to be a soundcheck for engineer Don Casale while the band waited for the arrival of producer Jim Hilton. However, Casale had rolled a recording tape, and when the rehearsal was completed it was agreed that the performance was of sufficient quality that another take was not needed.

found another one according to Wikipedia:

Roy Orbison - Pretty Paper

Recorded in one take with a 102 degree fever.  Roy was always a bad ass....

Bond song "Thunderball" by Tom Jones

found some in this article: http://www.popularmechanics.com/culture/music/a22237/sam-phillips-sun-studio/

Despite pushback from the artists, the famed mastered releases of Elvis' "That's All Right" and "Midnight Train" as well as Perkins' "Blue Suede Shoes" were all from the first take.

wow, found another tonight: http://ultimateclassicrock.com/the-knack-get-the-knack/

In early 1979, the band entered the studio with producer Mike Chapman to begin work on their debut. Get the Knack was wrapped up in less than two weeks. “I don’t think we did two takes on any song, except for ‘Maybe Tonight,'” Fieger once said. “What we had to do was make the record quickly,” added Chapman, “because to labor over it would have taken that spontaneity out of it.” Chapman’s production here is, as always, first class.

http://https://scontent-iad3-1.xx.fbcdn.net/v/t1.0-9/25507888_519476658420145_3385121873483692685_n.jpg?oh=7d394773a75820f403e7b73f78751776&oe=5AC5C586

https://en.wikipedia.org/wiki/The_Show_Must_Go_On_(Queen_song)

Mercury was so ill when the band recorded the song in 1990 that May had concerns as to whether he was physically capable of singing it. Recalling Mercury's performance, May states; "I said, 'Fred, I don't know if this is going to be possible to sing.' And he went, 'I'll fudgeing do it, darling' — vodka down — and went in and killed it, completely lacerated that vocal."

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according to this video:
http://www.youtube.com/watch?v=XJNm0PP_WrA

Sugarhill Gang, "Rapper's Delight"