I noticed while riding with someone today that his skewer was secured on the rightside of the wheel - I had never seen one anywhere but the left side. I mentioned to him that many (perhaps all - not sure - certainly the ones I use) bicycle tires are unidirectional, and if the wheel was mistakenly installed that way (it was that way when he picked it up from the LBS after a tuneup), perhaps he was running his tire in the wrong direction. I suggested that we stop and look.
I looked at my tire first to demonstrate the arrow indicating proper direction of rotation only to discover that when I had fixed a flat last week, apparently in my haste, I had installed my tire backwards. That brought up the interesting question as to why bicycle tires are unidirectional. I can understand many car tires being that way, because the tread is very specifically designed for that.
However, my Specialized Mondo S-Works tires are slicks - they don't even have cornering tread on the sides. Why would slick tires be unidirectional?