There are quite a few songs that incorporate rap even if their genre is not rap. In many songs, artists choose to use rap during the bridge or verses while the choruses remain sung. In "Perfect" by Pink, the bridge is completely rapped, and in "Billionaire" by Bruno Mars and Travie McCoy the chorus is sung by Bruno while Travie raps the verses.
Often when I'm learning a new song, I will speak out the rhythm in time before adding the music and melody in. Rhythms are, in my opinion, the most important part of the music-learning process. While doing this, it almost sounds more like rap as rap is very rhythmic in its nature. I decided to take a few songs that I knew and tried speaking them in tempo, but keeping the inflection and feeling of the lyrics, and I noticed that it didn't matter which genre I was performing in. I was then struck by the idea that, perhaps, many songs can be transformed into rap if more attention is given to articulating phrases, melody is removed but inflection remains, and a more straight forward and aggressive tone is implemented. I've posted a couple of my experiments to this post.
If Country and Classic Rock can be transformed into rap, what else would work? See how creative you can get!