Kinesiology Tape Benefits
This is in the discussion for quite a while. I have found no scientific studies which back the claims of kinesio tape. A review article (from which the quote below is taken) found no clinically important results which support the claims of the tape. The results about range-of-motion were inconsistant and it is not clear if the changes found were beneficial or not. They state:


  KT had some substantial effects on muscle activity, but it was unclear
  whether these changes were beneficial or harmful. In conclusion, there
  was little quality evidence to support the use of KT over other types
  of elastic taping in the management or prevention of sports injuries.
  KT may have a small beneficial role in improving strength, range of
  motion in certain injured cohorts and force sense error compared with
  other tapes, but further studies are needed to confirm these findings.


The study can be found here (links to the PDF):


Kinesio Taping in Treatment and Prevention of Sports Injuries


Other (also critical) studies are these:


A systematic review of the effectiveness of kinesio taping for
musculoskeletal injury.
The clinical effects of Kinesio® Tex taping: A systematic review.


The problem with these studies is that they are obviously not rigorous enough to make clear statements if KT is beneficial or not. Or (and this is also very possible) that the effect which is claimed to be there does not exist. Besides this, a placebo effect exists very well, since there is an intervention and also something present on the athlete. 

There is now a new study avalaible which is blinded and placebo-controlled. This study finds no benefits for Kinesio Tape above a placebo. The study can be found here, there is also a summary available here.