Wikipedia has a page devoted to the various claims that a particular religion is the fastest growing
http://en.wikipedia.org/wiki/Claims_to_be_the_fastest_growing_religion
Rather amusingly there are claims from various Christian denominations, Islam, Falun Gong, Budhism, Hinduism and even Wicca to this dubious honour and several more besides.
Why do people convert? Well I'm fairly impressed with some of the seperated twins studies which seem to show that people have a genetic tendency to be religious or not religious. If therefore someone with a tendency to be religious becomes disenchanted with their faith (or lack of it ) and someone gets to them at that time with a message they prefer they're likely to convert.
So why would they be disenchanted? A lot of Christian churches are rather caught in a liberal/conservative divide and will be making both conservatives and liberals unhappy. Islam is likely to appeal to conservatives especially those uncomfortable with the slightly more paganistic and polytheistic themes in parts of Christianity. (The trinity, Saints and statues,crucifixes and religious art , transmutation of the host all the hocus pocus)
Don't fall into the trap of thinking that all moslems are screaming jihadi-crazed sword wielding maniacs. Some Christians will think that way and when they find out that's not the case they'll be intrigued and be drawn in.
But I think JNO's absolutely wrong - I think there are a lot of people who join religions (and even more stay in them) for a sense of community - of being with like-minded people