There are a ton of music file conversion program out there. Many are good and many are not. Most offer free trials that allow you to try the program to determine if it fits your needs.
Some of these programs were made specifically for the file conversion only, other programs were music software programs that happen to have this file conversion utility as one of their many features. Song Surgeon, picture below is one such program. Song Surgeon can convert between the most popular file types including, mp3, mp4, wma, and wav.
It is important to understand that a good deal of the music available on the internet is restricted. That means that it cannot be opened.. and therefore cannot be converted to another file format, because it is encrypted. ITunes are one such example. Itune's files are stored as mp4, but unless you have the digital license that accompanied the original purchase of the mp4 song, you cannot play, or open or convert this song. Wma's are another file format that are commonly protect.
There are some ways to 'get around' the protection or encryption associated with some of the songs that are encrypted. For example, IPod's have an export feature on the player. Once you have loaded a song onto an IPod, if you export the song in an mp3 format from your Ipod to your computer, you will have removed the encryption and should now be able to play this on any computer or player.
The important thing to understand is that just because a program can convert a file format, doesn't mean it can convert the file you want to convert, due to the encryption or digital right management feature associated with most of the music sold over the internet.
It may be easier to rip a song from a CD. Once songs are ripped, they can be stored in any file format, wav, mp3, or anything else and these files ARE NOT protected and can easily be converted among the different file formats by Song Surgeon, or many of the other file conversion programs available.