My recommendation is a little cheesy, but songs from musicals are almost always pronounced clearly.  This is because the audience of a musical has to understand the words on the first try in order to know what's going on.  So, if you don't mind the cheesiness, musicals could be a great resource.  :)

A few entertaining musicals that I can think of off the top of my head are <em>Into the Woods</em>, <em>RENT</em> (the stage version soundtrack is better, but harder to find, than the movie soundtrack), and <em>Seussical the Musical</em>.  In the musical <em>Thoroughly Modern Millie</em>, there is a song that repeats the same text over and over, faster each time, so that could be helpful to listen to.  And if you're learning British English, the musical <em>My Fair Lady</em> is actually about a lower-class British woman learning to speak with a proper British accent.

I feel like this will get downvoted, but oh well!  I'm going to post it anyway, in case it can help you, or anyone else.

Country music is going to be more understandable because the songs are slower than say rap music or even pop. Also, country music has more of a story to tell so they will use a lot more words outside of the chorus verses. 

http://www.italki.com/entry/454515

I wouldn't pick a particular genre.

Any song from a native speaker singer should do, as long as it is not remixed and the voice is not computerized.

Songs with few or no vocal acrobatics are good. The less artistic, the better. They are easier to understand and they have practical vocabulary because they are made for mass consumption.

Very slow and very fast songs don't help with intonation, I think.

A good idea would be to hear the song once, find the lyrics, translate them (not word by word) for the general meaning and then listen to the same piece on loop