To clarify: this post is not particularly in response to anything that has been said so far, bar the OP, although I did read them. Mostly because everyone seems to agree with me so far.
Religion was invented for the purpose of control. It is a vessel used by smart neanderthalls to make people obey them by saying that if they don't they will eternally suffer and if they do they will be eternally rewarded. A tendancy to believe is inate in humans as a result of natural selection - if you question the priests you get impaled on a mammoth's tusk (whether or not it is attached to the mammoth depending on individual tribal cultures).
Traditions and cultures that stem from religion are largely in place to differentiate one groups followers from another. If a priest wants to declare war on another tribe he will need a religious reason to do so. It also helps to prevent your followers from joining another religion if that other religion's practices seem outlandish and satanic. Is it ok to eat cheese on a Tuesday if the moon is waneing? Since the average outsider would guess "yes", a religious leader could go a long way by making the answer "no".
Religion, therefore, is a method by which a social elite manipulate the majority. At least, it was origionally. I don't doubt that most modern priests genuinely believe. It can still, however, be used for control, and is being by the likes of Osama Bin Laden and Abu Hamza (please don't pick me up on spelling).
With regard to terrorism, the majority of the cause will be political, rather than religious reasons. The individual soldiers (I use the term loosely) will, however, be religiously indoctrinated and motivated because that is the chosen method by the terrorist leaders. Getting rid of religion would remove a large ammount of the labour from terrorism, but by no means all of it. Look at the IRA. They were not religiously motivated but they still had bombers. Notably, not suicide bombers. Blow yourself up and it's straight to the bottom of the class for you. Their bombs didn't kill many people either - they knew how to be a nuiscence by blowing up buildings, but they phoned in threats first and got the human inhabitants out. They were good terrorists; sort of a warm up for when al-quaeda got invoved. The point is, the IRA were more efficient and annoying than al-quaeda, but they didn't kill as many people, and therefore terrorism is better without religion.
I'd love to say more on what improves when religion goes away but I'm short on time so let's move on to reasons for keeping it. The main reason cited in general is that religion is what makes people be good. It is a reason for charity. I say bullshit to this. I'm an atheist. I give to charity on occaision, have done charity work, and don't go around raping and pillaging.
Religion can also help support people through drug addiction rehabilitation, etc. So can councelling. I don't think this outweighs the control and terrorism charges. I have to end here. Sorry. More to come I hope.