Of all the ones that are "speculated" about whenever this comes up, it's never them. So it won't be Cumberbatch or Elba. My fear is that they will go to the Sherlock cast, not for BC, but for Andrew Scott, who is a good actor but was a pretty ineffective Moriarty in that series. The BBC's own news page about this has a ridiculous list of possibles. It just takes someone to say "It might be Billie Piper" or "What about Helen Mirren" and it makes it onto their stupid list.
Last time I thought Richard Coyle would be a good choice but his moment has probably passed now. The speculation about bigger, more Hollywoody names is pointless. If they did a big feature film version then Depp might be pretty good, ditto Sam Rockwell. Equally silly is suggesting that a previous one would come back so forget about Tennant etc.
A while ago I'd have backed Damien Lewis but he's probably out of their league now with all his US success.
@matahari I think Hurt is portraying a much older version of the future Doctor for that story, I doubt he's the new replacement. Nah, as always it'll be someone none of us has thought of. @Eve While it wouldn't be Rickman I do think that darker "brooding" approach would be good for the next one, for a change.