Free Music Downloads

Can you legally download music from the internet for your computer or MP3 player? I have heard different thoughts on this. Some websites claim they provide free downloads but when you check into them there are costs involved. I think it works to copy a CD onto the computer and then transfer it to an MP3 player. Isn't it? I have lots of music but there is so much on the net that would be nice to have too. But I want to have it legally.