Should a CV for a fellowship application ever include test scores even if these scores are not requested? I did quite well on my GREs -- perfect scores on all three sections of the general test, and a result in the 98th percentile on the relevant subject GRE test. I'm applying for Ph.D. programs in a STEM field and will naturally submit these scores as part of my application.

However, I'll also be applying for fellowships like the NSF graduate fellowship and the Hertz. It's my understanding that these fellowships do not require the GRE, but I would assume these strong scores might work in my favor if the relevant committees were to know about them. Can/should I include these scores on the CV I submit with my application, or is doing so always considered gauche?
If you are going to cite your scores, then you should check to see if there is a reporting mechanism from ETS that will allow you to send official copies of the scores to the recipients. For instance, NSF had a "college code" so that you could send a report directly to them. Other fellowships may be similar.

One caveat that should be mentioned: if a university or fellowship specifically instructs you not to send something, don't send it. I know that some schools do not want and will not accept additional letters of reference, award citations, publications, and so on. If this is the case for the specific application you're completing, then you'll want to find some other way to provide the information. This might be in the form of a mention in one of your essays (if appropriate!), or in a "supporting information" box in the application.