Richard uses the word "proud" more than any other character in the play. He uses it to describe Henry Bolingbroke, England's soil, and his own majesty. It could be argued that Richard's obsession with pride is what ultimately costs him his kingdom. Even though he ends up humiliated, he never really escapes the sense that he deserves more – that as God's chosen ruler on earth, he doesn't really need to do anything to feel proud. In other words, Richard thinks he's God's gift to the world. Unfortunately, this keeps him from listening to advice that might contradict or criticize him, and leads him to mismanage the kingdom so badly that he eventually loses it.
When it comes down to it, Richard's pride causes him to lose his crown.
In Act 1, Scene 1, Richard says he "was not born to sue but to command," suggesting that his diplomatic effort to reconcile Mowbray and Henry Bolingbroke is an insult to his pride. This shows how weak he is (since he's already spent some time "suing," or begging, and it didn't work) and shows that he has a pretty fragile definition of a good ruler. If Richard had been more comfortable "suing," he might not have lost the kingdom.