A commenter recently suggested that if I wanted to believe in God and went looking for the evidence, I would find it. Nope. Tried that. It didn't work. Back at university I engaged in some great debates with theists, and I really wanted to believe in it. But a dispassionate look at the evidence really does favour the atheist point of view.
The first piece of evidence that Christians will point towards is the Bible. "It's a historical record" they will say. Evidence it may be, but it's not good quality evidence - it's all second hand. Stories passed along from person to person, distorted by time and translation and plucked from historical context. Let's contrast this with the evidence for quantum mechanics (which seems similarly ridiculous at first glance). This is real evidence - experiments which you can do to convince yourself even if you think the original experimenters lied about their results. Experiments which have been repeated all over the world and verified many times. That's real evidence. A book (even a very popular one) is not good evidence.
The next thing Christians will try is sheer weight of support - "two billion people can't be wrong" they say. Well, of course they can - there are also two billion people who are Muslims and Hindus, who the Christians will say are wrong. And another two billion people are either not religious or believe something other than "the big 3". So whatever the truth is, at least two thirds of the people are wrong about it. And even the 2 billion Christians can't all agree on which particular sect is the right one. Number of people is not good evidence.
The third thing is "the power of prayer" and religious people have lots of anecdotes about how prayer has helped particular people. Anecdotes are not evidence though - they suffer from selection effects. When theists pray for something and it comes true it is seen as evidence for God but when they pray for something and it doesn't come through it "must not be God's will for this to come about". If you do actual scientific, statistically accurate analysis of the power of prayer it turns out to have little or no effect. Any effect it does have is not proof of God anyway - it could just be a form of placebo effect.
The fourth is "religious experiences" - people who claim to have seen or touched God, or to have had very powerful feelings of being close to a magnificent, benevolent power. I used to find this argument extremely compelling (and was quite jealous that I hadn't experienced it myself) but I have since discovered that similar effects can be induced in the brain with magnetic fields or drugs. Like the power of prayer, this is something else that is "entirely within the mind". Chemical imbalance in the brain seems to be a much more likely explanation for these experiences than God.
These seem to be the main arguments. There are a number of minor ones as well but they mostly seem to have logical flaws like taking their conclusion as an initial assumption.
There are some very compelling arguments against God as well. The main one is Occam's razor - positing the existence of God doesn't actually explain anything (not even the creation of the universe, as God Himself then has the same origin problem). So we can get a theory of the universe that is simpler (and therefore more likely to be correct) by not including God.
Another thing that I found very convincing is the geographic distribution of different religions. People tend to believe the same things as their parents, friends and neighbours. This suggests that religion is passed on from person to person like a meme rather than having any intrinsic truth. Dawkins poses an evolutionary explanation for this strange human behavior - there is an evolutionary advantage to believing what your parents tell you. This behavior started out as a way for advantage-giving wisdom like "don't eat these particular berries" to spread to one's offspring but because historically we had no way of verifying these memes, incorrect but (mostly) harmless memes like "pray to the great invisible being for healthy crops" also sprang up and took advantage of the same mechanism.
A third argument against religion is how contradictory it is. Surely if there was a God and He wanted us all to behave in a particular way, he would have made the bible very coherent and hard to misinterpret. It is none of these things, as we see from the number of people who misinterpret it to forward their own agendas constantly. In fact, religious dogma seems to be particularly effective as a tool for powerful ruling classes to exert control over the general population, which suggests that it evolved to be that way for exactly that purpose.