The original series was well before my time, and it's not one of those shows that was widely syndicated, at least not in my area when I was growing up. So I have no firm attachment to the original show besides watching the movies.
IMHO, I thought all of the actors caught the essences of their characters.
Chris Pine was not Shatner, but IMHO that's a good thing. The essence of Kirk was his rebellious, suave, bravado I guess you could say, and I thought Pine pulled that off well.
Spock is all about logic vs. emotion, and I imagine a younger Spock fresh into StarFleet would have had a much greater conflict between his human and Vulcan sides. I think Zachary Quinto did an excellent job.
Uhura wasn't that fleshed out for me in the movies. But the gist of her seemed to be a very caring, intelligent person, and I think given that she had the least firm template, Zoe Saldana did a great job.
To me, Karl Urban nailed DeForest Kelly as Bones, at least the Bones that was in the movies. IMHO, he was really like a younger version of Kelly.
Simon Pegg was kind of goofy as Scotty, but I think Scotty was kind of goofy to begin with.
Anton Yelchin and John Cho I think did good jobs as Chekov and Sulu. For me, Chekov was mainly an accent. Since Yelchin did a pretty decent job there, he worked fine for me. Sulu was kind of this all-around every man for me, and I think Cho did a good job with that.
Now because I didn't see more than a handful of episodes of the original series, I don't have these rigid ideas about who the characters are in my head. I know for others, when they think Kirk, they immediately think Shatner, etc. So for me, I was much more open to the idea that Kirk could still be Kirk without being Shatner.
I could really buy each of those actors being the younger versions of their characters. And I would definitely look forward to seeing how they were fleshed out in future movies or a TV series.
"Vincere scis, Hannibal, victoria uti nescis" -- Maharbal, 216 B.C.E.