Just an FYI, rap did not become popular of its own merits and appeal. It should have been a passing fad just like disco, new wave, grunge, ska and everything else we've seen over the past 20 or 30 years. The reason it's still around is that people are going to like whatever they hear on the radio or see on MTV the most. Doesn't matter what it is or how good it really is, if people are inundated with it, they'll eventually become fond of it.
So how did rap become such a mainstay on the airwaves? Well, since the beginning of the music industry, the record companies have used very mob-like tactics to ensure control over what people are exposed to and in what quantities. They also employ the same tactics to get their artists to do exactly what they want. However, the whole "gangsta rap" thing provided a bit of a problem. Those guys didn't have a problem walking into an exec's office or showing up at his house with a few friends and threatening to kill the guy or his family if their music didn't start showing up on the radio and TV.
That's what makes rap different than almost every other kind of music... they turned all the gangland strongarm crap around on the music industry.