Attracted by Jay Ballou adding an answer, I'll add my £0.02. If Bruno Ranschaert had not already done so, I'd have mentioned Knuth's "Structured Programming with GOTO Statements" article.
One thing that I've not seen discussed is the sort of code that, while not exactly common, was taught in Fortran text books. Things like the extended range of a DO loop and open-coded subroutines (remember, this would be Fortran II, or Fortran IV, or Fortran 66 - not Fortran 77 or 90). There's at least a chance that the syntactic details are inexact, but the concepts should be accurate enough. The snippets in each case are inside a single function.
Note that the excellent but dated (and out of print) book 'The Elements of Programming Style, 2nd Edn' by Kernighan & Plauger includes some real-life examples of abuse of GOTO from programming text books of its era (late-70s). The material below is not from that book, however.
Extended range for a DO loop
do 10 i = 1,30
...blah...
...blah...
if (k.gt.4) goto 37
91 ...blah...
...blah...
10 continue
...blah...
return
37 ...some computation...
goto 91
One reason for such nonsense was the good old-fashioned punch-card. You might notice that the labels (nicely out of sequence because that was canonical style!) are in column 1 (actually, they had to be in columns 1-5) and the code is in columns 7-72 (column 6 was the continuation marker column). Columns 73-80 would be given a sequence number, and there were machines that would sort punch card decks into sequence number order. If you had your program on sequenced cards and needed to add a few cards (lines) into the middle of a loop, you'd have to repunch everything after those extra lines. However, if you replaced one card with the GOTO stuff, you could avoid resequencing all the cards - you just tucked the new cards at the end of the routine with new sequence numbers. Consider it to be the first attempt at 'green computing' - a saving of punch cards (or, more specifically, a saving of retyping labour - and a saving of consequential rekeying errors).
Oh, you might also note that I'm cheating and not shouting - Fortran IV was written in all upper-case normally.
Open-coded subroutine
...blah...
i = 1
goto 76
123 ...blah...
...blah...
i = 2
goto 76
79 ...blah...
...blah...
goto 54
...blah...
12 continue
return
76 ...calculate something...
...blah...
goto (123, 79) i
54 ...more calculation...
goto 12
The GOTO between labels 76 and 54 is a version of computed goto. If the variable i has the value 1, goto the first label in the list (123); if it has the value 2, goto the second, and so on. The fragment from 76 to the computed goto is the open-coded subroutine. It was a piece of code executed rather like a subroutine, but written out in the body of a function. (Fortran also had statement functions - which were embedded functions that fitted on a single line.)
There were worse constructs than the computed goto - you could assign labels to variables and then use an assigned goto. Googling assigned goto tells me it was deleted from Fortran 95. Chalk one up for the structured programming revolution which could fairly be said to have started in public with Dijkstra's "GOTO Considered Harmful" letter or article.
Without some knowledge of the sorts of things that were done in Fortran (and in other languages, most of which have rightly fallen by the wayside), it is hard for us newcomers to understand the scope of the problem which Dijkstra was dealing with. Heck, I didn't start programming until ten years after that letter was published (but I did have the misfortune to program in Fortran IV for a while).