How do you pick a graduate supervisor?

I wrote a post about how to pick an undergraduate supervisor, and many of those recommendations still apply.

For a superb and more in-depth description of what you want in a supervisor (scientific and mentoring ability) see this paper by Prof. Ben Barres.

And an accompanying paper about how to be a graduate advisee by Prof. Indira Raman :).

It might also be useful to check out this site's post on what questions to ask graduate students during interviews because quite a few of the questions on that list pertain to interactions with supervisors.