So much for the US #1 - for our Dutch audience, this is the Wikipedia pagewith Top 40 #1 hits (starting in 1965). For some silly reason, the hits are ordered alphabetically by artist. At the bottom of the page, you can look them up by year.
 
So it wasn't the Beatles with Yesterday, which topped the charts only in November, but the Rolling Stones with (I can't get no) Satisfaction.

Sugar Shack was penned by a guy who lives (or lived) in Craig, Colorado.  I don't recall his name, but he owned a club in that town and the bands stayed at his place.  I played there in '83.
 
As for the song, if I recall it was a typical teenage bubblegum tune from the early 1960s..
 
John

I'm leaving it up to you by Dale and Grace.
 
Unfortunately, my birth was around an hour after JFK was murdered, so nobody really cared what was #1 on the charts that day.

Stop, in the Name of Love
 
Not TOO bad...but I was hoping for a Beatles tune...

Sugar Shack was written by Keith McCormack and Faye Voss and perfored by Jimmy Gilmer & the Fireballs.  Interestingly, the Fireballs, without Jimmy Gilmer, were a Tex/Mex instrumental band, similar to the Ventures, featuring George Tomsco, who was apparently an influential guitar player in that style.  Tomsco also played on some posthumous Buddy Holly releases.  The surf tune, Bulldog, is by the Fireballs as well as the tune Torquay.  McCormack, in addition to writing tunes for Gilmer and the Fireballs, was a member of the The String-A-Longs, another Tex/Mex group, and also played guitar on some Buddy Holly releases.  The String-A-Longs, Fireballs, and Buddy Holly, all recorded at Norman Petty's studio in Clovis, New Mexico.

Tossin and Turnin by Bobbie Lewis. never heard of it.
The Everley brothers' temptation in the UK charts.
see here
 
Graeme

Where's Wing when you need her?  
 
The Chipmunk Song by David Seville & the Chipmunks.  
 
Keith

Thanks John and Dave. I still can't work out if I've ever heard the record..

See if the memory stick kicks in...
 
..There?s a crazy little shack beyond the tracks  
And ev?rybody calls it the sugar shack  
Well, it?s just a coffeehouse and it?s made out of wood  
Expresso coffee tastes mighty good  
That?s not the reason why I?ve got to get back  
To that sugar shack, whoa baby  
To that sugar shack.  
 
There?s this cute little girlie, she?s a?workin? there  
A black leotard and her feet are bare  
I?m gonna drink a lotta coffee, spend a little cash  
Make that girl love me when I put on some trash  
You can understand why I?ve got to get back  
To that sugar shack, whoa baby  
To that sugar shack, yeah honey  
To that sugar shack, whoa yes  
To that sugar shack.  
 
Now that sugar shack queen is a?married to me, yeah yeah  
We just sit around and dream of those old memories  
Ah, but one of these days I?m gonna lay down tracks  
In the direction of that sugar shack  
Just me and her yes we?re gonna go back  
To that sugar shack,  
Whoa uh oh  
To that sugar shack, yeah honey  
To our sugar shack  
 
(Fade)  
 
Yeh, yeh, yeh, our sugar shack ..

Lonely Boy by Paul Anka....
 
It wasn't an omen, really. Sometimes I feel lonely because so few people think the same way I do.
 
JP

JP
I like your perspective.

Alone Again (naturally).
 
heh.

Bad, Bad Leroy Brown by Jim Croce  
 
 
 
'Nuff Said

I Can't Get No Satisfaction..7-23-65