I think Dexter is right in pointing out that while science mostly deals with the material and religion/spirituality with the immaterial, it's clear that both have something to say about the other. One who believes that water can become holy and that bread and wine can become the body and blood of Christ clearly have certain beliefs about the material world and its interaction with the immaterial. Similarly, science can very quickly fall in the realm of ethics and morality such as in genetics. I would argue that morality and ethics are mostly spiritual issues in the sense that we are dealing with judgments of the spirit or mind if you prefer.
Cliffy also mentioned how important it is to distinguish religion from spirituality. I'll second that.
While science is older than the scientific revolution (think of some Greeks who managed to predict eclipses and properly estimate the diameter of a spherical Earth), let's say for clarity's sake that science really started with the scientific revolution.
In the pre-scientific world, religion ruled the global zeitgeist. Acts of God were everywhere. If one nation's army conquered another, it was because God was on the side of the winner. Sickness was interpreted as godly punishment or testing. Lighting in the sky was caused by Zeus. One was considered untouchable because of one's supposedly bad actions in a former life etc. etc. etc.(Unfortunately, some of what I mention still happens today).
The point I want to make here is that those who are caught in the net of dogmatic religion fail to properly differentiate objective (exterior) from subjective (inner) reality. Depictions of God as a bearded white guy sitting on a throne are a clear example of this confusion. A father who kills his daughter because she has fallen in love with a man of different religion is another. There are countless examples. The recurring pattern is the failure to see how one's subjective conceptions about reality are literally projected on the screen of ''objective'' reality. One confuses his worldview with the world itself. In other words, it's a failure to understand that the outside world is relatively independent from whatever happens in our human minds.
Science helped to change all that. We now know that lightning isn't caused by Zeus or God. It has no ''intention''. Science helped us in drawing a line between ourselves and the outside world. It helped us understand that the outside world has its own mechanisms and that while our inner world is still very real as a subjective phenomenon, it must be differentiated from the outside world.
With that in mind, it is my view that science is superior to dogmatic religion in the sense that it represents a more mature relationship between our minds and the world.
That being said, we all need a spiritual assessment of what is happening to us. While it's important to differentiate between subjective and objective reality, that doesn't mean that both aren't connected. And it certainly doesn't mean that subjective reality is any less real than objective reality. Dreams and nightmares clearly demonstrate this. The fact that a nightmare can wake you from sleep, with your body full of sweat and a feeling of overwhelming terror is testament to the reality of our inner life. There was no real shark biting my legs off, but my experience of it was real enough for it to have awoken me. The hallucinations of a schizophrenic might not correspond to what is happening out there in the objective world, but the hallucination itself is as real as anything else. The point being that whatever our worldview is, we all have one and it's impossible not to.
We are all spiritual beings. Not in the esoteric sense of us having spirits that survive physical death but in the sense that we all experience the inner reality of spirit which can not be described in terms of velocity, mass and space.
To sum it up, spirituality and science are compatible. They need one another. But it's important to differentiate the two. Science is a tool and in the end, it is our spirituality that will determine what we decide to do with it.