During their press event today Paramount put out their video press kit, which includes four new clips from the Star Trek movie. They are already online and they are viewable below. All are extended versions of scenes from trailers, but in one case it is a bit spoilery so tread carefully. [UPDATED w/ higher res videos]
Kirk meets Uhura
Kirk flirts with Uhura in a bar in Iowa.
Enlist in Starfleet
Kirk and Pike have a chat after a bar fight (same Iowa bar).
Kirk, Sulu and Olsen prepare for their orbital dive over Vulcan
What gives you the right [extra spoilers]
Capt. Robau of the USS Kelvin meets Nero and Ayel aboard the Narada.
B – roll — Behind the scenes.