Star Trek II is an apt example (in more ways than one).
A major plot point of that movie is about how Kirk believes himself better than death. How he was able to beat the "no-win scenario" by cheating, and that Kirk simply didn't believe in the "no-win scenario."
By the end of the movie and Spock's death, Kirk realizes that he "knows nothing:"
"I've cheated death, tricked my way out of death, and patted myself on the back for my ingenuity. I know nothing."
He makes the realization that there ARE no-win scenarios, and this time, his friend paid with his life for his arrogance.
Despite the flashy ship battles in Star Trek II (tame by today's standards), most of the action occurs between the people, and inside of the people.
This is true for most Star Trek films (the latter two being obvious exceptions). Star Trek was always about a humanist exploration of not only space but of the human condition and all of its possibilities. The resolutions found at the end of TV episodes were not as much "oh good, we saved the world/galaxy/universe," as much as it was a resolution or exploration of a major moral/ethical question.
The new Star Trek films have shot that aspect out the airlock and opted for more a "big explosions in space" approach. It certainly sells movie tickets, but it is a great perversion of Star Trek's roots.
There's nothing inherently wrong with liking the new Star Trek movies. But as Cerrax pointed out, they are terrible at carrying on the Star Trek legacy.