This is, in my experience, the most frequently asked question about asexuality (although usually people use a euphemism). Here is my straight answer:
Presumably you are not so much interested in my personal life, but interested in whether asexual people in general masturbate. Unfortunately, answering the question directly would not satisfy your curiosity, because A) you don't know whether I am representative of asexuals, and B) you probably don't have any idea how much non-asexual people masturbate either.
What you really want is some capital-letter SCIENCE!
No, really. In general, it is very difficult to scientifically quantify asexuality, but it's relatively easy to just make a survey asking how often people masturbate. Someone must have done it.
I'll save you time. A survey was hidden in this paper by Prause and Graham.
(From Table 2) Frequency of masturbation:The followup question that everyone asks is...
asexuals: 3.7 +/- 2
non-asexuals: 4.5 +/- 1.9
The scale is from 1 (never masturbated) to 7 (4 times/week or more)
But how can that be?
Forget how things can be the way they are. They just are. We've shown it empirically with SCIENCE!
But presumably you meant to ask, how is this consistent with the definition of asexuality? An asexual plus sexuality equals not-an-asexual, am I right?
No, that's the wrong definition of asexuality. Asexuality does not mean a lack of sexuality, it means a lack of sexual attraction (or sexual interest or sexual desire--the definitions vary). In other words, there are multiple dimensions of sexuality, and asexuality just refers to one of those dimensions. One of the reasons asexuality is so hard to study is because suddenly it becomes necessary to disentangle all these different dimensions that people usually assume go together. Masturbation and sexual attraction are two of the easiest dimensions to disentangle; even a survey can do it.
Other frequent questions: Do asexuals think of it as a sexual activity? What do asexuals masturbate to?
Unfortunately I don't think this is in the scientific literature (you may scan it for yourself). Based on the accounts I've seen, nearly all answers are possible. Asexuals may think of it as sexual, or not. They may masturbate to objects, concepts, people, or nothing in particular. If that seems strange... I am not really sure what is meant by a non-strange sexuality. Anyways, it is hard to tell whether this is statistically different or similar to non-asexual masturbation habits.
Another frequent question: Is it strange or creepy of me to ask about this?
Not strange, no. It is creepy though. It was probably also creepy of me to answer.