Arabic Music Translation
The website http://www.arabicmusictranslation.com/ has over 800 songs from over 175 artists from all over the Arab world. The site contains both transcriptions of the songs in Arabic and translations into English. Look up and listen to a song in Arabic while reading the words in Arabic first, then in English.
LAFLWSP - Learn Arabic with Songs
The "Learn Arabic as a Foreign Language with a Studied Plan" website has a few songs (with video) mostly from cartoons, but they are translated and have the Arabic as well, so you can follow along. They also point out certain useful phrases from the song and then replay it so you can understand it better the second time. The songs and grammar are not too complex.
The Arabic Student Blog
One post on the Arabic Student blog talks specifically about music and suggests 15 songs that he thinks Americans might tend to like. http://www.thearabicstudent.com/2012/10/top-15-arabic-songs-for-americans.html
Free Music Downloads
You can also download Arabic songs for free from http://www.last.fm/music/+free-music-downloads/arabic. Then you can put them on an mp3 player and listen to them throughout the day and pick up more Arabic without any major effort! I find that the more I listen to a particular song, the more I am able to pick up vocabulary and the more I understand it. So having music on an iPod is a great tool for me for language learning. If I can translate the song into English and listen to it, that helps even more.
Music on Youtube
You can find all sorts of Arabic music, including music videos on Youtube. Cairokee is an Egyptian band that has some great songs, including one that has become known as "The Song of the Egyptian Revolution," (referring to the 2011 Arab Spring). It's called, "Sout Alhoreya" or "The Voice of Freedom". This band's music sounds a bit more western to me than some of the more traditional Arab music, which you may like or not like.
You can find the lyrics to the song above at this link: http://yallaarabic.blogspot.com/2011/06/sout-el-7ouriya-voice-of-freedom-nezelt.html
Here is the Arabic version of the song "Waving Flag". It's partially in Arabic, partially in English and it has subtitles throughout with transliteration of the Arabic, and the English translation.
Here is another song by Cairokee that has English subtitles.