I do think that people have a spiritual need, but if you do not believe in God you define spirituality in a different way. When I think of spirituality, I mean the best ideals of the human spirit. It's usually defined by religious belief, because that is how most people define morality and spirituality, it's what they know, but that doesn't have to be the case.
For example, I believe in being honest. I am not honest because I believe God will punish me, but because I think it's the best way to be, it's part of my personal code of conduct. Being spiritual for me means working towards those ideals, being my best self and reaching my full potential. I spend a fair amount of time thinking about these things and making sure my outward actions match my inner code of conduct.
I also meditate every day, which helps keep me from getting off track and involved with things that don't mesh with my beliefs.
As Ghandi said, "you must be the change you wish to see in the world. "