I first saw Kenneth Branagh at a very young age in HAMLET at the Barbican. It was a formative experience. Here was an actor that made Shakespeare come alive because even if you didn't understand the details of what he was saying, the way he spoke his lines and the emotion with which he expressed them made them completely comprehensible. His performance was devastating. I've never since seen a standing ovation like the one that ended the play, flowers being thrown at the stage, the audience in tears.
Fifteen years later I've been to see him again in Chekhov's IVANOV as part of the Donmar's season at the Wyndham's Theatre. This story of a man blighted by depression and emptied of feeling is unsettling. In fact it frequently references the Danish Prince, Ivanov describes himself as a 'hand-me-down Hamlet'. But Branagh perfectly communicates the complexity of being caught in a downward spiral, crippled by the achievements of his youth, self-indulgent and yet somehow immensely empathetic. The third act is a tour de force and there are moments when he hits a level other actors rarely reach onstage.
Now, I'm aware that he became the poster boy of the luvvie set when he was married to Emma Thompson, that he has made some dodgy films (MARY SHELLEY'S FRANKENSTEIN for one) and that he can get it wrong (his performance in David Mamet's EDMOND at the NT in 2003 couldn't lift a badly out-of-time play), but when he's on form no-one can touch him. It was interesting that he was pitted against Tom Hiddlestone as the self-righteous Dr Lvov, a young actor who has the potential take on his mantle as Britain's finest stage performer.
Otherwise, I'm not convinced we have anyone coming through who's as strong. Ben Whishaw is often cited as someone to watch, and did an acclaimed Hamlet himself recently, but is there anyone else you would nominate?