I often hear among people who are only vaguely familiar with Star Trek referring to the character of Spock as 'Dr Spock', getting confused with the author of the book about children. It got me to thinking though: Spock is a pretty clever guy and it wouldn't surprise me if he had a PhD. My question: Does Spock actually have a PhD? If so, what is it in?
He's never referred to as Dr Spock, or as having a PhD, in any of the Star Trek series (source: the second of the two links below). So there's nothing to say he did have a PhD, but also no canon confirmation that he didn't.
We also know that Spock rejected an offer to attend the Vulcan Science Academy in order to attend Starfleet Academy. I suppose he could've earned a Ph.D. at Starfleet, since he did do at least a little bit of postgraduate work, but most evidence is pointing toward no.
Look, we know Spock is a really smart guy, but that's no excuse for being underqualified. Without a doctorate you're probably not going to get a lot of papers published, so where are you contributing to the scientific community? At the very least Spock made it much harder on himself to gain any credibility for his findings among other scientists.
While you need a large breadth of knowledge in your field to obtain a Ph.D, you also spend a significant portion (2-8 years) of the time working towards it by writing your doctoral thesis, which is incredibly specialized.
Much of what the Enterprise deals with is new phenomena (as well as new lifeforms, new chemicals, new plants, etc). In these cases, a specialist may be of less value than someone with a lot of general knowledge.
In addition, specialists would probably be assigned to ships and locations that would make use of their specialization. Write a thesis on a new theory for warp design and Starfleet would probably have you work in warp design. Write a thesis on an aspect of plant biology, work on in a research station, etc.
UPDATE: Star Trek Encyclopedia (a canon source) confirms that the dialogue below is specifically a reference to Benjamin Spock. For posterity (and in the event the snippet of dialogue is useful to anyone else in the future), the original answer is directly below.
In the Voyager episode "Ex Post Facto", the Doctor is considering a name for himself, and has the following conversation about it with Kes:
KES: Pick a name you like, perhaps from someone who inspires you.
EMH: Dr...Dr. Galen... Dr. Salk... Dr.—
KES: (interrupts) Those are good.
KES: Can you see yourself with any of those names?
EMH: Not exactly.
This gives canon confirmation that Spock holds a doctoral degree.
As for the discipline that this degree represents, there is no explicit mention in any Star Trek works. He demonstrates a broad scientific expertise aboard the Enterprise, and so this degree could represent astrophysics / cosmology, exobiology, mathematics, computer science, or some combination of these.