Copyright protection on music typically lasts throughout the life of the composer from the time the work was created until death plus another 50 years thereafter or 75 years from publication or 100 years from creation. Let's make it clear: when you download copyrighted MP3 music, you pay for the privilege of listening, not owning.
But there are different types of music materials you can download for free because they are in what is called the public domain. They belong in the realm of royalty free music. There are either not copyrighted or have gone beyond the prescriptive copyright ownership period for the laws on intellectual property protection to apply. Musical materials like sound effects are normally not copyrighted. Classical music composed earlier than 1930 as well as theme songs and background music from old films can also be royalty free by this time and are free to download. But new performance of these royalty free music it not.
Be wary though that not all free downloadable music online are royalty-free. Some musical materials are offered as sample music from budding musicians and artists who promote their artistry by allowing their performances or compositions to reach the most number of people by offering them for free download without any obligation. Even established musicians and celebrities often offer free samples of the forthcoming albums. But let there be no mistake, these are copyrighted works and copying their musical line or lyrics in part or in whole exposes you to lawsuits for copyright infringement.