Is this necessary? Can atheists claim to be spiritual? What does it mean, if anything, to be spiritual outside a religion?
The essential nature of spirituality is a reverence for life. The heart of it is sacredness. This is an important concept that is often neglected. Religions are quick to adopt something they call sacred, but religions such as Christianity and Islam squash honest reverence into the dust and ascribe it all sorts of horrible, crazy adjectives, like unnatural, evil, and profane. A reverence for life is anything but profane. It is the exact opposite. A reverence for life is an acknowledgment of sacredness, a deep appreciation for it. Nature, including human nature, should be seen as sacred, not when it submits to some deity's drunken demands, but, rather, when it lives by its own right, according to its own changing needs and desires.
Life abounds with sacredness. Love is sacred. Beauty is sacred. Harmony, symmetry, and infinity are all sacred in some way. Anything that puts you in a state of awe because of its wondrous existence can be considered sacred.
Think about science and math. Scientific truths are often incredibly sacred when expressed in simple terms. The simplicity of relatively advanced (pardon the pun) equations like E=MC2 or of simple equations like 2+2=4 can leave us in a state of jaw-dropping amazement. We are tempted to say, like our fellow theists, "Someone out there must have created this."
Yet, because we are atheists, because we have faced reality and freed our minds from the artificial constraints of religious belief, we can see how much more beautiful the world becomes when there is no incomprehensible deity hovering over us, calling the shots. We can see how much more beautiful is the idea of natural, self-directed emergence in evolution. Sentience is sacred.
To be spiritual, in its truest form, is to revere all that life has to offer. It is to accept life for what it is and, yet, at the same time, to encourage it, using the unique capabilities that come with the enhanced awareness that life has provided us, and that we have struggled to give ourselves as humans, to become something better. Can atheists claim to be spiritual? The answer is an unequivocal yes.