We can!

We can see spirits while out of body, and during other altered states of consciousness, such as in meditative trance.  We may see spirits in the dream state as well.

I believe it is also possible to see some spirits while in normal physical consciousness if the spirit being is close enough to the physical dimension.  Think about all of the ghost sightings there have been throughout history.  I'm sure they're not all bogus. 

The idea is that spirits are not generally seen because they are not generally here.  Most spirits rise onto higher dimensions of existence after physical death.  We may get glimpses of those who linger around the near-physical planes, but perceiving into higher dimensions while physically awake is no easy task, especially when many of us are so fixated in this one dimension.