Ewan--yes, in the U.S. and Canada someone can sue you to prevent you from performing their song. If a court enjoins you not to perform it and you defy the injunction, I wonder whether you could go to jail for contempt of court. At least in principle. (If you have to go to jail, doing so in principle is probably the best.)

Ditto to Tim. However, composers may not be able to stop people from performing their songs if they sign up with ASCAP or BMI. I don't know how that works.

Dick, you own the copyright the minute you write the song. (However, you might find it hard to gain any benefits unless you register the copyright with the government. You might find it hard to collect any royalties if you don't turn over the collection to ASCAP or BMI--and maybe even if you do, I don't know.)

Earl, there are possible problems even if money never changes hands. A copyright allows you to prevent people from performing your work if for some reason you don't want them too; it also allows you to require performers to give you credit, and to prevent them from changing the work.

(I'm not a lawyer. All this is from my understanding of Terry Carroll's Copyright FAQ.)