Those of us who reject the view that only analytical propositions can be necessary are sometimes challenged to give examples of necessary synthetic truths. It should first be pointed out that one is not required to give any such examples in order to refute the claim that only analytical propositions can be necessary. Given that such a view is self-defeating, we are justified in affirming that there are non-analytical (synthetic) necessary truths. Providing examples of necessary synthetic truths will only add an additional layer to an established fact of metaphysics/epistemology.
In any case, here are a few synthetic truths I take to be necessary:
Metaphyics: Out of nothing comes nothing.
Epistemology: In order for a subject S to have knowledge of some external object E, there must be a causal relationship between S and E.
Ethics: It is wrong to torture children for fun.
Aesthetics: "Hey Jude" is more beautiful than "Pants on the Ground."
The usual objection, to the latter two at least, is that there are instances in which children, "Hey Jude," and "Pants on the Ground" do not even exist, so propositions containing these referents cannot be necessary. However, this conclusion would be too hasty. Even in the absence of these referents, it would still be necessarily true that "Hey Jude" would be more beautiful than "Pants on the Ground" if they existed, etc.
Of course, a relativist will not be persuaded by this point, but that's not my problem. :)