Depends on the country - in the UK you can/could go straight from completing an undergraduate degree to working full time in research doing a PhD without having to attend any more classes.

http://en.m.wikipedia.org/wiki/Ludwig_Wittgenstein#section_6

At the urging of Ramsey and others, Wittgenstein returned to Cambridge in 1929. Keynes wrote in a letter to his wife: "Well, God has arrived. I met him on the 5.15 train."[123] Despite this fame, he could not initially work at Cambridge as he did not have a degree, so he applied as an advanced undergraduate. Russell noted that his previous residency was sufficient for a PhD, and urged him to offer the Tractatus as his thesis. It was examined in 1929 by Russell and Moore; at the end of the thesis defence, Wittgenstein clapped the two examiners on the shoulder and said, "Don't worry, I know you'll never understand it."[124] Moore wrote in the examiner's report: "I myself consider that this is a work of genius; but, even if I am completely mistaken and it is nothing of the sort, it is well above the standard required for the Ph.D. degree."[125]

-- The story in a nutshell.