I cleaned some badly corroded Buffalo Nickles using SOS pads in the sink, followed by a Dremel tool with a brass wire wheel, and finally using some Dremel fine polishing compound and a small buffing wheel. I'll take some pictures when I get home tonight. They turned out real well.
Silver coins: I just rinse them under the sink and lightly pat dry. Rubbing or wiping them can cause scratches. I once used a small amount of lemon juice to remove some green corrosion from a silver quarter where it had been against a nickle in the ground for many years, and that seems to work good.
If the coin has any collectors value (key date, gold, etc) I wouldn't touch it. Some places may even pay more for it in "as-found" condition versus an improperly cleaned coin.
I still haven't found a method for cleaning pennies that I like. Olive oil is slow but seems to get good results. Other methods can remove too much dirt/corrosion when can leave the penny with a pitted look.