Cyclops shouldn't die because it's not part of his character. It's like having Wolverine marry Belladonna, or Bishop using shapeshifting to stealthly infiltrate an enemy establishment.
Jean Grey is supposed to die. It is part of her character arc to die, and be reborn as the Phoenix. But it's not part of Cyclops' character to die. Yes, he's died before in the comics. Lots of characters have. But their death was never "real". They always came back. And coming back, in these films, does not fit in. With the real world setting they have, having people die off and coming back resurrected later on doesn't work. Again, it works with Jean Grey because that is a special trait of her character. And there have been a few discussions on these forums alone as to how her rebirth can be explained to fit into this story line. But the most important part is the fact that dying is part of Jean Grey's character arc. It's not a part of Cyclops' arc.
That's the difference between Obi-Won Kanobi, the example always used when people say "nobody complained when Obi-Won died"... well, Star Wars didn't have pre-existing source material that it had to stay true to... Lucas was able to do whatever he wanted to tell the story. X-Men, on the other hand, has pre-existing source material that it needs to remain true to, and killing of Cyclops is not remaining true to that source material.
So no, Cyclops should not die. Neither should Xavier. However, I don't think that Xavier's death would be quite as bad for me as Cyclops' death. Though I am totally against it, I feel that Xavier's death could be rationalized, and in the end, possibly work. Cyclops' death would ruin the movie, and consequently the franchise, for me.