I prefer an author to try to categorize their book to the best of their ability, and I imagine most agents feel the same way. The bottom line is that this saves us time when evaluating queries, especially since many can then be dismissed easily if they are in a category we don't handle. It also allows us more time to then evaluate the queries that are in the categories that we do represent and are actively looking for material.
I don't think there's anything wrong with mentioning more than one category, since the reality is that most books could fit in multiple genres. I wouldn't say it makes the book seem more versatile though, since multiple category classification is commonplace.
I also can honestly say that while numerous categories are of interest to me, their are only a few that really get me excited right now. This could be because I think the market for this category is hot right now, or I just read an article on a similar subject, or in what little spare time I've had I've been reading books in that genre. As a result, I'll look at those queries immediately, as compared to perhaps putting them off until later (i.e. end of the day or end of the week).
Oh, and I also like to hear who you think your work compares favorably to, for the same reasons as above. For example, I'm more inclined to be excited if you say your mystery is comparable to Lehane than Martini.