Idris Elba would be great - but as has been pointed out, he's a little too old to start three of four films.
Aside from him? Given screen Bond barely ever qualifies as a fixed character, and is more a rather bland icon, there's no reason why there couldn't be a female Bond (so the character could finally achieve something artful and challenging, i.e. an opportunity to explore gender roles and perceptions of masculinity, femininity, maleness and femaleness) - and Rosamund Pike would easily be my top pick. Going from Bond 'girl' to Bond would be an endearingly freaky twist on continuities and casting, and she could absolutely nail the whole 'impossibly English sociopath' aspect to the icon.
...hell, Eva Green would've been amazing, but that would be pushing things a little too far.
As for blokes to continue a boringly blokey role? Tom Hardy and Tom Hiddleston are two popular ones, and whilst I like Hardy in other roles I think he'd be a poor Bond (actually, no, he'd at least be better than Connery, Moore, Brosnan... have I mentioned I really don't like James Bond?). There's an inherent unhinged cruelty to the character/icon, and I think Hiddleston would be far better suited to play off charm/smarm with a dispassionate aptitude for violence and murder.