Let's consider the absolute to your question, would the world would be a better place without religion? An assumption must be made, however. The assumption being that "religion" refers to organized religion as opposed to people's inherent spirituality (belief in a higher power, fascination with the unknown, the inner voice of good vs bad, etc.).
So, what would this world be like with no organized religion? I think it would be worse off even with the fact that most every war, most every major atrocity throughout history can be attributed to religion either directly or indirectly. The problem WITHOUT religion is that, unfortunately, human nature on the whole consists of people who need some sort of guidance, some sort of direction, some sort of way to relate to others. It's quite possible that people NEED that guilt, they need to be reminded that God is watching their every move and if they're bad they're going to hell. Otherwise, there would be many people, those more inclined to be of the lemming nature, who would gravitate to having no moral compass.
Churches, some more than others - Mormons probably the most, donate time and money to those in need. They help influence people to really care (through public prayer requests). They bring people together as they ponder life's bigger questions (even though religion never gets to the true heart of the matter).
Despite its shortcomings, religion for the most part inspires a lot people to be better people - and if not, to at least STRIVE to be better people.