Of course violent conquest isn't the only means of religions spreading, the other major one is spread along trade routes. The slow conversion of Indonesia to Islam is a good example of this, where local traders and royalty begun to adopt the religion in attempts to allow favourable relations with trading partners.
And there is no doubt Islam, and all religions, offer their followers something. In earlier times trade of course tended to flourish amongst people who decided to share a religion, and there are obvious advantages to adopting the same religion as your rulers. But on a more fundamental level religions try to offer people many different things: a central purpose, a sense of belonging to a group, ethical guidance, consolation and of course eternal life.
In modern times religions don't generally try to out compete each other through violence, but rather fight it out in the minds of potential followers. Well designed religions, which are the most compatible with the underlying machinery of the human mind, are always likely to out-compete ones which are not so well designed in this respect. Perhaps the best place to see this is in the landscape of American Christianity, where different Churches compete for followers is quite brazen ways, mimicking modern marketing techniques. A similar thing happens everywhere, but usually in a more subtle way.