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
                                                   (I.i.24-30) 

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. 

Richard is the stereotype villian though endeared by his verve and perspicacity. Is he the 'product' of heredity or environment? His mother laments:

Thou cams't on earth to make the earth my hell.
A grievous burthen was thy birth to me,
Tetchy and wayward was thy infancy;
Thy school-days frightful, desp'rate, wild, and furious,
Thy prime of manhood daring, bold, and ventrous;
Thy age confirm'd, proud, subtle, sly and bloody

                                           (Act IV.iv.167-172) 

Innate perfidity and lust for power are 'perfected' through choice. Having no sayso over his entrance into life, Richard orchestrates his own interpretation of felicity and well-being:

I, that am curtail'd of this fair proportion,
Cheated of feature by dissembling nature,
Deformed, unfinish'd, sent before my time
Into this breathing world, scarce half made up,
And that so lamely and unfashionable
That dogs bark at me as I halt by them;
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

                                                   (Act I.i. 9-30) 

In his warped value system are echoes from the witches in 'MacBeth': "Fair is foul and foul is fair."