In one of the clips posted at TrekMovie.com, we see Kirk acting a lot like the womanizing Kirk from the original series. Downsized the spoiler-text below:
The clip begins with Kirk meeting Uhura at a bar. Apparently trying to hit on her, Kirk inquires as to what Uhura is studying at the academy, whereby she replies with Xenolinguistics. Uhura doesn't believe Kirk knows what it means, however he replies that it's among others the study of alien languages. In a very Kirk fashion, he comments that Uhura is "Good with her tongue". At the end of the clip, a Starfleet officer asks Uhura if Kirk is bothering her. Uhura replies that she can handle him. Kirk replies that she can "handle him anytime". The clip ends with Kirk calling the officer "cupcake", and suggesting the officer bring a few more friends so that it will be an even fight between Kirk and the officer+friends.
Not willing to spoil too much, from the little i've seen, I think Chris Pine got Kirk's "mannerisms" down solid. And judging by the comments i've read, written by both Trek fans, and non Trek fans, we may indeed be in for an enjoyable movie in the coming month.