Why do you never see any other planes in the sky whilst flying? I was just wondering as I passed the airport this morning why, whilst we are flying, do we never see any other planes nearby? There must be millions of planes and millions of people flying each day, I appreciate the sky is massive but these planes must follow roughly the same routes so how is it that they never seem to pass by any other aircraft?
If you're not seeing them, you're not looking. 

I see planes all the time when flying commercial.  Obviously, I see them a lot more when close to a major center, and a lot less when in the sparse parts of the Pacific Northwest (Montana, Idaho, Oregon, Washington).

I think spotting them may take some practice. Visually, a plane 10+ miles away is a very small dot, and easily missed.   Try looking for contrails and be sure to look at altitudes above and below you.  Scan the sky in narrow, 10&deg;  concentrated "fields of view" to scan from left-to-right all the way across the sky.