When I was a young and impressionable graduate student at Princeton, we scared each other with the story of a Final Public Oral, where Jack Milnor was dragged in against his will to sit on a committee, and noted that the class of topological spaces discussed by the speaker consisted of finite spaces. I had assumed this was an "urban legend", but then at a cocktail party, I mentioned this to a faculty member, who turned crimson and said that this was one of his students, who never talked to him, and then had to write another thesis (in numerical analysis, which was not very highly regarded at Princeton at the time). But now, I have talked to a couple of topologists who should have been there at the time of the event, and they told me that this was an urban legend at their time as well, so maybe the faculty member was pulling my leg.

So, the questions are: (a) any direct evidence for or against this particular disaster?
(b) what stories kept you awake at night as a graduate student, and is there any evidence for or against their truth?

EDIT (this is unrelated, but I don't want to answer my own question too many times): At Princeton, there was supposedly an FPO in Physics, on some sort of statistical mechanics, and the constant $k$ appeared many times. The student was asked: 

Examiner: What is $k?$

Student: Boltzmann's constant.

Examiner: Yes, but what is the value?

Student: Gee, I don't know...

Examiner: OK, order of magnitude?

Student: Umm, don't know, I just know $k\dots$

The student was failed, since he was obviously not a physicist.

This happened just last year, but it certainly deserves to be included in the annals of mathematical legends:

A graduate student (let's call him Saeed) is in the airport standing in a security line. He is coming back from a conference, where he presented some exciting results of his Ph.D. thesis in Algebraic Geometry.  One of the people whom he met at his presentation (let's call him Vikram) is also in the line, and they start talking excitedly about the results, and in particular the clever solution to problem X via blowing up eight points on a plane.

They don't notice other travelers slowly backing away from them.

Less than a minute later, the TSA officers descend on the two mathematicians, and take them away.  They are thoroughly and intimately searched, and separated for interrogation. For an hour, the interrogation gets nowhere: the mathematicians simply don't know what the interrogators are talking about.  What bombs?  What plot?  What terrorism?

The student finally realizes the problem, pulls out a pre-print of his paper, and proceeds to explain to the interrogators exactly what "blowing up points on a plane" means in Algebraic Geometry.
