GM,
Here is where you get into personal preference as to sound.
I am an advocate to not compress ANYTHING unless you absolutely have to.
When you compress something like drums you have to be real careful to not take the snap and life out of them. Yes limiting the peaks will help more often than not to keep transients from clipping your mix, but once you get beyond that you get into an area where it is a trade off. More compression brings up the body of the sound but kills the transients making a dull mix.
As to whether you should compress individual pieces, I usually treat the kick and snare individually (when needed) , but the toms and cymbals as a whole to keep the image from shifting around weirdly as it will sometime when compressing individual toms and such independantly from the overheads.
When I need really thick drums what I will do is copy certain tracks (like the kick , snare and toms) and set them up on a seperate aux bus and compress them as much as I can before they die and then sneak THAT mix up under my regular drum mix to fill it out a little (or a lot). That way you retain the snap and sparkle of your original tracks and can add some beef up under it to taste.
Hope that helps some, I am sure someone will rip me a big one saying I don't know what I'm talking about ( ;p ) but none the less it really works.
Tom