Good answers, but nobody seems to have mentioned yet that some timber types are very prone to grain raising, and some really are not.
I have never "raised the grain" by dampening as a separate process, but I have seen the effects of this raising after applying a water-based base coat. From my (admittedly limited) experience, denser hardwoods seem to be less prone to the grain raising or "fluffing" up, but this may not be true in all cases.
Also, it actually depends on what kind of finish you want. See this link:
Is grain raising (with water based products) something to be concerned about?
In short - no, but it is a question of personal taste. The grain doesn't feel rough to the touch, it's more of a textured feel. In other words the pattern of the wood can be felt through the wood finish. Some customers really like to be able to feel the wood. If several coats of varnish are being applied then grain raising is not really an issue because the varnish tends to seal over the grain that has been raised, thus creating a smooth surface.
It's also worth considering that if you're going to be applying a finish with more than one coat, it's often the case that the timber will be sanded between coats anyway. With Meranti timber (which is a somewhat light hardwood which is quite prone to fluffing/raising grain) we would apply a base coat, sand it to key the finish (which also has the effect of flatting the grain) and then apply a topcoat, and be left with a nice smooth finish. It does mean that the denibbing/keying phase of the finishing process takes a bit more effort, but the need for raising the grain as a separate process is removed.
I wouldn't say "don't bother", but I would think about the type of finish you're trying to achieve, and whether it is worth it on the particular type of wood you're using.
As with most types of finishing, I would suggest you try it with and without this process on a scrap piece of timber and see the effects for yourself.