Becket is played admirably by Richard Burton; Henry II is portrayed by Peter O'Toole. Both were nominated for the best actor Oscar, but neither won. In addition to these nominations and the best screenplay award, the film was nominated for nine other Oscars, running the list from costumes, music, directing, best picture, and a best supporting actor nod for John Gielgud, whose cameo as the King of France is rather interestingly presented.
Indeed, the movie has a remarkable realistic feel to it, particularly for a film from the 1960s, when cinema was as likely to portray stylised and idealistic images of the past. The sets are in bare stone with a minimum of ornamentation, as would have been the case in Plantagenet times; likewise, the ceremony around the royal person is much less grand, and the church rather grand, which is both accurate and serves to highlight the underlying conflict of the story in the film.
Becket is portrayed as a man of ambiguous loyalties -- a man of principle who has yet to find principles worthy of loyalty. Finally, in the role of archbishop, he finds a calling from the honour of God (and in so doing is not unlikely many priests who see their path to ordination as the means of spiritual grace; indeed, many are disappointed that the faith does not come with the office). Whether Thomas Becket actually experienced a spiritual conversion that made him a strong champion of the church, or in fact saw the power of the church as a means to an end of dominating the country, we will perhaps never know.
In the film, Becket is often disparaged as being a Saxon; this is perhaps overstated, given his Norman lineage, which is never hinted at in the film. While he does not come from Norman nobility, he is far from being a simple Saxon. Burton's portrayal of Becket shows the change from worldly chancellor to spiritual archbishop in unsubtle terms. Even so, there is an ambiguity that plays out marvelously in both his performance, and the reactions of the other characters who constantly question his sincerity.
O'Toole's performance is not as polished as Burton's; when he plays an older, wiser Henry II in 'The Lion in Winter' four years later, the acting is much more dramatic and effective. It perhaps goes without saying that Pamela Brown does not make the same impression on the screen as Eleanor of Aquitaine as Katherine Hepburn does in the later film, but Eleanor is an incidental character in Becket in any case.
Music in this film is not a prominent feature -- various trumpet and brass flourishes announce events or major scene changes in parts; a lot of chant (long before Gregorian chant achieved popular status) accompanies church scenes -- indeed, I credit this film for giving me my first real taste of Gregorian chant. The scene with Sian Phillips as Becket's love Gwendolyen is accompanied by period string instruments -- again, Phillips is a remarkable actress who is under-utilised in this performance.
Done in a flash-back manner, there is a resolution in the film -- Becket is dead, made a saint, honour is satisfied as the King does penance, and the people are happy. We know what is going to happen, but then, anyone with knowledge of history would likely know the story already. In fact, Henry's reign was rarely without challenge, but he was always powerful, and much more effective after Becket's death than before. Reigning for nearly twenty years after Becket's death, he left a very powerful Western European coalition of lands that soon fell apart, and embroiled England and France in war for centuries later. The tensions between church and state carry forward to this day; while the specifics of the challenges faces Becket and Henry II are very different from issues today, the principle of the relationship between church and state is far from definitively resolved.
Also, the side-line issue of class warfare and racial prejudice (teased out with subtle nuance between the Normans and Saxons, who, ironically, look exactly the same on the screen) are addressed in an interesting, pre-civil rights sort of manner. This issue is never resolved in the film, as indeed it wasn't in the 1960s, either.
This is an intriguing film, with great acting and great production values, and an interesting story that, even if not completely historically accurate, does not alter the history so much that it becomes a parody of the subject.