Intellectual property laws in the U.S.A. assert that if you composed it, it is yours by default. An automatic legal right. Canada and England have similar legislation.
Although various commercial services claim that their brand of copyright documentation is superior to what is available at no cost to the musician, when push comes to shove (a legal battle), it is all about who can afford the slickest lawyers to represent their case.

A recent case transpired in Canada with Sarah McLaughlin and the gentleman who produced and co-wrote four of her songs. The album was released without any songwriting credit to her producer, and no royalties were paid out to him. He had clear legal claim to co-writing the songs - she could afford a better lawyer.
Last I heard, he is still not receiving royalties, and cannot afford to hire lawyers to appeal the decision.

Bottom line: almost any legitimate corroboration of the fact that the song is yours will do, as long as you can afford the legal muscle to follow through should someone contest your ownership.

My approach: write the songs - have some fun. If you write a winner and someone "steals" it, relax and write another winner...