The main reasons I hold my belief in the religion of Islam to be true are its compatibility with common sense and the overwhelming amount of outside evidence in favor of it.
Unlike other religious groups that define faith as something you engage in despite facts (a "leap of faith"), I see it as a return to objectivity and reason that is, first and foremost, based on facts.
The first fact I am referring to is the utter helplessness and dependency of mankind on forces outside our control, and the seemingly perfect ordering of everything in the natural world to our advantage even though cosmically we are only a speck of dust and a blip in time.
The second is the existence of individuals throughout history who succeed against all odds in calling their people to worship a wise Creator whom they claim to be sent by, and whose teachings become guiding principles in the minds of billions of people of different races, cultures, and languages.
There are many, many more signposts but these are the most obvious.
Specifically about Islam, I researched the religion before I embraced it and found the exact opposite of what its detractors say. I found a moral teaching superior to all others containing no contradictions with science or reason. Every theological or moral problem that used to trouble me had an answer in Islam, and not only that, but usually in the most ancient sources.
The clarity and "take it on face value" character of Islam was very satisfying to me in a time of my life I was experiencing a lot of confusion. There are no baffling paradoxes in Islam, or ranks of mystic knowledge to climb. It's about accepting simple truths, like the Oneness of God, reality of death, etc. into your heart in deeper and deeper ways, and a sense of communion based on that that transcends millenia and unites continents.
Also, as a side note, there's a very important fact that atheists / agnostics dismiss too easily, which is the answering of prayers. Until you yourself have been in dire need, prayed for something improbable, then received it from a direction you didn't expect, you can't understand the effect that experience has. It's easy just to say, "you're imagining it," or, "confirmation bias."
I am not the type of person to enjoy religious flame wars, just posting for those who are curious.