Well there are only a few that I recommend and use. Remember these apps are free and you should never pay for the below apps.
The first program is called G-Tunes Music Download MP3 aka G-Tunes Music Lite aka MP3 Downloader and it’s more widely known. They’ve changed the name several times. It has a wide variety of features and overall I love it. The interface of G-Tunes has changed over and over again but it still works. G-Tunes music will save your music to /mnt/sdcard/media/music . Nice to know that path.
This second one is clean and just landed on the Market but it will probably be pulled soon; I hope not. I like the simple interface and over all it seems less bulky. This app did a better job at getting the songs with the lyrics than G-Tunes/MP3 Downloader; maybe I got lucky. The apps is responsive and tell you the site it’s download it from. It’s called Music Download by Liu Xuan. Music Download by Liu_Xuan will download your music to /mnt/sdcard/musicdownload .