A lot of people think you have to go through a long and expensive legal process to get a song or a book or whatever copyrighted, but you really don't. If you compose a hit song and it gets recorded by a popular singer, a publishing company will usually handle the legal rights for you. The idea that another songwriter down the hall with his own guitar will copy your song word for word is mostly a myth. Only a handful of songs will even get heard by a music label, anyway.
About the most important thing an official copyright does for a songwriter is establish a date of creation. If someone else composes a song that uses similar chord progressions and lyrics, a songwriter can prove in court that he or she wrote the song first.