Donald E. Knuth answered this question in the book "Literate Programming", 1992 CSLI. On p. 17 there is an essay "Structured Programming with goto Statements" (PDF). I think the article might have been published in other books as well.
The article describes Dijkstra's suggestion and describes the circumstances where this is valid. But he also gives a number of counter examples (problems and algorithms) which cannot be easily reproduced using structured loops only.
The article contains a complete description of the problem, the history, examples and counter examples.
