I submitted my paper on mathematics to a journal 8 months ago but I have no received any reports or comments yet. I sent an email to the editor asking him about the manuscript, he just replied that it is still under review. What shall I do?
Mathematics tends to have a long refereeing process. It's nice when it can be completed in a few months, but eight months is not especially worrisome. The editor should be sending the referee(s) periodic messages to make sure they aren't just forgetting, and you can send status inquiries to the editor every once in a while if you'd like (it shouldn't be necessary, but it can't hurt and could conceivably help). I tend to ask for a status update every six months or so.
One reason it takes so long is that refereeing a mathematics paper is difficult. The referee has to read and understand the proofs, which is one of the slowest and most painstaking forms of reading. Another issue is that there is no expectation that it should be done quickly: a referee who takes eight months isn't generally considered problematic by the journal or the community at large.
In practice, the lengthy refereeing times are not a problem. Mathematics papers are typically circulated publicly (for example, on www.arXiv.org) long before they are accepted for publication, so the publication process isn't holding up progress in the field. And the mathematics community is well aware of how long it takes to get papers officially published and takes this into account in career evaluation (hiring, tenure, etc.). For example, if you're applying for a job, nobody will expect your papers from the last year or two to be published yet. If they are at least on the arXiv and submitted for publication, then everything is as it should be.
To reiterate the other good answer and comments... do nothing. It is unfortunate, yes, and frustrating, yes, and inconvenient, yes, that refereeing takes so long... but it is both understandable and inevitable.
Ironically, but understandably, the more original your work is, the more effort will be required of referees... who are paid nothing, and will acquire no status/raises/funding/whatever from their efforts to appraise or improve your writing.
As in other answer/comments, hiring committees and funding agencies are aware of the time-lags... although, yes, true, it's better to have gotten through this gauntlet than have to explain that one is enduring it.