In order to approach an understanding of whether Gloucester's character in Shakespeare's Richard III qualifies as a villain, the term "villain" requires a bit of clarification. When a character is a "villain," it most often refers to someone who shows no sympathy or concern for others and someone who will stop at nothing to reach his or her goal. For the purposes of Richard III, this definition proves rather fruitful.
As for the first part of the definition, namely the idea that a villain cares for no one other than himself/herself, this certainly appears to apply to Gloucester. He is very manipulative of those around him, even toward those in his own family. Gloucester, however, does care for other people. His caring nature, however, cannot interfere with his larger goals. He truly sees those around him as friends (or quasi-friends). Gloucester's attitude does not change until he has cause to believe that their loyalties are in question. Though he is not a very caring individual, Gloucester does care, but only when it serves his purposes.
Taking the second part of the definition, namely that a villain will stop at nothing to attain his/her goal(s), it requires very little to indicate how Gloucester falls into this category. From the very outset of the play, the reader/viewer understands that Gloucester aspires to the English throne, and it serves as the driving force behind all of the actions he takes during the play. Being the fifth in line for the throne, he makes sure that three of the four are "eliminated" from contention. The fourth dies before Gloucester can do anything. Gloucester, even when he attains the crown, fights to maintain it - ultimately against Richmond at Bosworth Field.
Ultimately, when taking these two factors into account, Gloucester would certainly qualify as a villain in the larger scheme of things. His villainy, however, seems to stem from the political situation in which he finds himself.