Romantic relationships between faculty members and students are often depicted in movies or books, and the student falling in love with his/her professor seems to be a bit of a cliché. But how common are such relationships in practice?
I've found a rather old survey (1982) of David L. Rowland, Larry J. Crisler and Donna J. Cox that claimed
Of the 184 respondents (59.8% female and 41.2% male), over one-third of both sexes reported flirting with their instructors, while 46% of females and 32% of males felt that instructors had flirted with them.
Flirting is, of course, is not the same as a romantic relationship. Patricia A. Rupert and Deborah L. Holmes (1997) survey earlier studies of the sexual relations between faculty and students:
in a survey of 807 male faculty, Fitzgerald, Weitzman, Gold, and Ormerod (1988) found that 26% of the 235 respondents reported having sexual encounters with students; in a similar study of 483 male and female psychology professors, Tabachnick, Keith-Spiegel, and Pope (1991) obtained a rate of 11%. Although there was a considerable difference in these rates no doubt in part due to the inclusion of female faculty in the second survey - both indicate that sexual encounters between faculty and their students are commonplace on our campus
One notable example is the marriage of Professor Philip Bobbitt (Princeton (A.B.), Yale (J.D.), and Oxford (Ph.D.)) and Maya Ondalikoglu,Columbia Law School graduate.
I think the closing votes are because of the statistics and the "notable examples" the OP wants, but this is an important ethical and psychological issue specific to academia.
With regard to the issue, I came across this paper by Prof Higgins published in 1998. One key issue seems to be the age difference between the teacher and the student. The second point is the drama it creates in the mind of the student, which is supposed to be focused on learning.
We [teachers] should be responsive to the fact that one of our students is going through a drama that will affect her learning and ought to be heeded in the handling of the relationship. This does not mean that we should treat a student’s avowal of love as something which calls for a life decision on our part. To do that would be to respond in kind and to lose sight of the fact that classrooms are in part like the playground of the analytic situation, a place in which we can express ourselves without every utterance leading to immediate action. When someone is in process, and you have devoted yourself to witnessing and facilitating that process, you are wary to treat as definitive any one version of the evolving being before you.
It is unlikely that faculty members at graduate schools will be punished for just having a romantic relationship. But frequent problems in romantic life will surely be noted by colleagues and some curb be introduced when the academic pursuits of the prof suffer heavily.
I don't have references and statistics, but I know of one MIT PhD who later married their advisor and now they are both tenured faculty in the same department. They did divorce later in life, but that doesn't seem to have outwardly affected their working relationship.
Nobody talks about it much; it seems like a nonissue, although perhaps it was different before the dust settled. She never changed her name, so you probably wouldn't know they'd ever been married if you weren't close enough to know they have teenage children together.