Great question - and one central to the play. Traditionally, Richard has been seen as a Vice figure (and indeed, he himself makes the comparison in 3.1 - to 'the formal Vice, Iniquity'). Traditionally, the Vice carries out evil acts purely out of malice.
But Shakespeare's Richard is clearly at odds with a world that disregards him because of his disability:
Why, I, in this weak piping time of peace,
Have no delight to pass away the time,
Unless to spy my shadow in the sun
And descant on mine own deformity:
And therefore, since I cannot prove a lover,
To entertain these fair well-spoken days,
I am determined to prove a villain
Richard states quite clearly (here and in Henry VI) that his malice and frustration stem from his disability.
But in that last line is the crux of the problem. Is Richard arguing that he is PRE-''determined'' to become a villain: that his disability and evil are one and the same thing, and visited upon him by God? Or is he saying that he himself is ''determined'' in terms of motivation?
Is it the world's prejudice that is the root of Richard's evil - or is it his own? As ever, in Shakespeare, it's left open.