There are two possible interpretations of this question:

1. Can you trigger an exposure with the lens removed:

   Answer: It's camera specific. Try setting the camera to manual mode. On my Nikon D80, it will not take an exposure with the lens removed except when in full manual ("M" on the mode dial).

2. Can you take a meaningful or interesting image without something acting like a lens.

   This is where things get tricky. For instance, I would argue that anything that projects some sort of pattern of light onto a surface (in this case, the sensor), effectively is a lens. Therefore, unless you want a flat, monochromatic exposure, you have to have some sort of lens.
   A pin-hole lens (as described by Hasin Hayder in his answer), is still arguably a lens, even if it is not a refracting lens. As such, you cannot shoot a meaningful image with out some manner of lens, even if it does not communicate with the camera, as lenses specifically designed for your camera do.