I hope I don't have to explain who Captain Kirk is. If I do, it's possible you're on the wrong blog.
I will go into how he died a bit though. First, you should know we're talking about the old Kirk -- William "Priceline" Shatner. Shortly after retiring, Kirk is asked to attend the maiden voyage of the USS
Enterprise-B (this is
Star Trek Generations, btw). On that voyage, they receive a distress signal from two ships caught in a strange energy ribbon. The
Enterprise is able to save them, but becomes caught itself in the ribbon. To free them, Kirk has to go engineering and alter the deflector shields.* He is successful, but just as the
Enterprise escapes, the ribbon makes contact with the engineering section causing major damage. When the crew recovers, they find a gaping hole in that part of the hull, and Kirk is gone.
That was Kirk's first death. It's not bad (we'll talk about why in a second), but it wasn't his
real death. See, the ribbon imprisoned Kirk in a time nexus.* Decades later, Captain Picard finds Kirk and convinces him to return to the present to help Picard stop a madman from destroying the sun of Veridian III. Kirk goes with him and together they are able to distract the villain long enough to thwart his plans. In the process, however, Kirk is wounded (or falls off a bridge -- they tried a couple versions) and dies.
* Star Trek science.
Before I go into why Kirk's death was lame, let's talk about what makes a character's sacrifice work. It's not enough that a character dies for someone (or goes to prison for them, or gives up their chance at becoming a rockstar, or lets them have the last tater tot, etc. -- sacrifice can mean a lot of things). If you want the reader to admire the character's compassion, their sacrifice has to be IMPORTANT, it has to be RIGHT, and it has to be NECESSARY.
The character has to sacrifice for something important. It has to matter, and it has to be in proportion to what the character is giving up. If Jack risks his life so that his buddy Bonzo can win the National Texas Hold 'Em Tournament, that's not very admirable. On the other hand, if Bonzo needs to win the tournament so the mob won't kill him and his family, Jack's sacrifice is a lot more worthy.
The character has to sacrifice for what's right. Readers sympathize with characters that are doing the right thing. Jack's sacrifice for Bonzo's family might be important, but if his "family" is a child prostitution racket, well... no one's going to give Jack any awards.
The character's sacrifice has to be necessary. If there was an alternative, but the character chose sacrifice anyway, no one will admire it. If all Jack had to do was loan Bonzo some money, we're going to think he's stupid, not noble.
Let's look at Kirk's deaths now and see if we can figure out what went wrong. First his death on
Enterprise-B. Important? He saved the lives of many people, so yes. Right? The people he saved were (so far as we know) good people. Check. Necessary? The movie set it up such that Kirk had to be the one in engineering (at least, there wasn't time to explain it to someone else -- in any case, if he sent someone else to do it, he'd have been a jerk). Check.
It was a good death for a character as big as Captain Kirk. Later, when you find out Kirk's alive, it's kind of cool. He survived! That's just what such a great captain deserves, right? But then he died again. Was his second death important? Technically. He saved lives, though we were never really made to care about the Veridian people, so it's arguable. Was it right? Again, we were never really
shown any Veridian characters. While we assume they are innocents, to the reader they are faceless. Yes it was right, but only technically. Necessary? Arguable. Kirk knew what Picard was asking was dangerous, but from a story standpoint, there's no reason Picard needed Kirk to pull it off.
Kirk's second death hit the right points (important, right, necessary), but it hit them weakly. After all the dangers he had been through, readers expect a death in proportion to the character. A minor character dying for the same reasons might have been a worthy sacrifice, but this was James T. Kirk. It was made worse by the fact that we already thought Kirk had died, and his first death was
more worthy than his second.
But it's okay, because we can learn something from it. If you want a character to be admired for their sacrifice, make it important, right, and necessary. And if you bring a character back to life, make sure his second death is more important than his first.
J. J. Abrams, I'm looking at you.