"What sluggards, what cowards have I brought up in my court, who care nothing for their allegiance to their lord. Who will rid me of this meddlesome priest."
Henry II might have wished he had not spoken those words, since he shut himself off for forty days of mourning and penance as soon as his knights disposed of Thomas a Becket, the meddlesome priest to whom he was referring. What's more, he had to perform two public penances, crawling on his knees in sackcloth and ashes before permitting himself to be flogged by monks.
Thomas had been Henry's closest ally in the Church ranks, eventually becoming Lord Chancellor in the King's court. He remained a canon in the Church, though he never really dressed the part (or acted it). He himself acknowledged he was a vain man, more attentive to birds and hounds than to souls in need of guidance.
The death of Theobald, Archbishop of Canterbury, pushed Becket into the spot he had been trying to avoid, one from which he must choose between Church and King. He warned Henry not to push for his appointment, because he would be forced to defend the Church against the royal prerogatives. He also asked the Pope not to appoint him, since his friendship with Henry would divide his loyalties. Both ignored his request, believing that Thomas could handle the conflict and keep everyone happy.
I suppose that it worked out well for the Pope in the long run. The subsequent few years were rocky, while Thomas was hiding from Henry in France and England was being run as the King wanted it. Thomas eventually returned to Canterbury and fought back, prompting the King to mutter the words written above, and his knights to rush off to the Cathedral for an abduction. Thomas refused to be abducted, and was therefore chopped against a pillar between a pair of altars. He was fast-tracked to sainthood while the King was forced into total contrition. In that regard, I suppose the Church held the victory and Henry lost the round.
Then again, if we step back for an even longer view, Henry II would eventually be portrayed by Peter O'Toole while Pope Alexander III was played by Paolo Stoppa (Who? Exactly!). So I suppose everyone came out a winner in the end. The film, by the way, is Becket -- well worth watching, though if you could only choose one film where Peter O'Toole plays Henry II, it should definitely be Lion in Winter.