Reviewing is completely voluntary in all senses. I don't know the percentage of research active mathematicians who have ever reviewed for MathReviews or Zentralblatt, but it is certainly bounded away from 100%. It is relatively rare for a research mathematician to write reviews in any quantity over a period of more than a few years: I think it's something that many of us try out for a while but don't stick with in the long run. For a personal touch, I am a 2003 PhD, I have written about five math reviews, and I have gotten overdue notices on about four more. I would rather write nice, insightful reviews for half of the papers that I get sent, but I haven't yet figured out what do about that.

I agree with Tim Porter that, as a graduate student, you should discuss this with your advisor. I think that if any of my students asked me about it, I would mildly discourage them from writing reviews, for the following reasons:

(i) It is not closely enough related to your thesis work to be a good use of a mid-to-late career grad student's time.

(ii) Prospective employers are generally not going to be more excited about your application because of the reviews you have written.

(iii) Most graduate students -- even ones who have already done some research work of their own -- don't have a broad enough perspective to write insightful reviews. (Or, more positively put, they will have a broader perspective later on and will probably write only a bounded number of reviews in their life no matter when they start.)

Finally, I should say that refereeing papers is a totally different story. I feel that it is an ethical (and karmic) responsibility to referee at least as many papers as one submits. A graduate student can make a good referee for some papers, because they are less likely to feel that it is beneath them to read the paper line by line and really make sure it is correct.