What date goes on your hardbound PhD thesis?
This is the kind of question which is best answered with actual evidence. Many American universities have their thesis formatting rules online, and you can find them with relatively little effort. British Universities (Oxford and Cambridge, in particular) often seem not to give as detailed rules. From these examples, it is clear that the rules for which date is used depends on the university. 


Harvard University:  "[Month and year of the submission of the completed dissertation to the department, division, or committee and Dissertation Acceptance Certificate was signed]",
MIT: "the date the degree(s) will be conferred (June, September, or February only)",
Stanford University: "(Date should reflect month and year of submission to the Office of the University Registrar.)"
University of Michigan: "year of degree conferral not year that dissertation was finished" (they don't want a month).
University College London: no date seems to be required on the thesis (none is mentioned in the guidelines, and there are theses without dates in their archive). 
University of Edinburgh: "Year of presentation.
In the case of a thesis which is resubmitted, the year in which the
thesis is resubmitted should be shown as the year of presentation." What do they mean by "year of presentation"? From their website: "At some point between submission of your thesis and the viva, you are encouraged to give a final presentation of your work to the School, often via a research group seminar series."
University of Leeds: "the year of submission
for examination (Or resubmission where the thesis is submitted following re-examination after referral)."