Dry Hopping

I have a general idea about what this is and how to do it, but can this be done with any beers? Or generally do you only want to do them for full flavored beers, or are there 'prefered' beers to do this with?
Is the only benefit of dry hopping to make it more bitter, or does it add aroma/flavor?

Dry hopping will not impart any bitterness to a beer; in order to get more bitterness, the hops have to be boiled to isomerize the acids. Dry hopping basically adds additional hop aroma to a beer. I personally like the effects of dry hopping.

Usually this is done with pale ales and similar styles, but it isn't just limited to those styles.

This is the method that I use to dry hop, to get the most out of the hops:
Let the beer ferment in primary for a couple of weeks (for a normal strength beer), then rack to secondary. About 3 days before I bottle, I will add typically an ounce of dry hop (hop style dependent, not all hops can be used as dry hops). Don't add the hops when active fermentation is occurring otherwise the volatile hop aromas will be gone with the CO2.

If you just want to get a feel for what dry hopping can do for you, add two ounces of Centennial or Cascade to an American IPA. Just drop the pellets into the fermentation vessel and rack the beer into it with the yeast. Sit on it for two weeks, then keg or bottle.

This is a really simplistic way of dry hopping. Yes, you'll lose some of the benefit from the yeast being so active and bubbling it out with the CO2, but you'll get the idea. Then if it's something you find you really like, you can get more careful with the process (and I completely agree with avidhomebrewer in the post above on when to start the process). You can add the pellets directly to the brew (but you'll have more trub which will have to drop out of the beer in the bottle/keg). You can put the pellets into a sack with something heavy to keep it below the liquid level, like marbles (sterilized). You can buy a hop diffuser, which is a little ball or cigar-shaped holder for hops, made of stainless steel screen material.

If you don't care for it, though, at least with the quick method I list above you'll not be spending time and money finding out.