In 2007 when I was in physical therapy after a bad car accident, I had a therapist use this tape on my wrist where i had a bone bruise (compression fracture). I was supposed to leave it on as long as it would stay on, up to 3 days. I ended up taking it off after a day. It seemed to be doing nothing other than looking stupid and annoying me.
In March of 2011 when I was preparing for my first half marathon I bought some of the tape at my local sports store. My ankles had been bothering me, I had plantar fascitis and was also trying to avoid blisters. I tried putting it on the way the instructions showed and again it was uncomfortable and looked ridiculous. At that time I finally researched the tape and could find no science whatsoever to support its use. I ended up wrapping my ankles and feet with regular sports tape for that race. The regular tape helped to hold down the swelling while I was running and avoided blisters. Outside of that it had no use. It did not aid in avoiding any injury unless you consider blisters and injury.
With so many sports products on the market it is important to do your research before wasting money on them. It is frustrating to see so many athletes using products like this because it does make the general public trust the product at their word and it causes people to waste money and risk injury thinking that something like brightly colored tape is going to help.