Even though each movie has it's own stand alone plot, I don't think that any of the 3 movies work on their own.
X-Men doesn't really work on it's own, because there's no closure to anything at all. The movie ends with Wolverine going off to find his past, and Magneto promising to escape his prison and continue to fight the war against humans. X-Men leaves too many unanswered questions.
X2 answers those questions, as we are taken deeper into Wolverine's past, and we see Magneto indeed escaping his prison to continue fighting the war. But then, it only raises more questions. For comic book fans, the resurrection of Jean Grey. The X-Men in the White House, truly becoming the X-Men. In X-Men, it seemed as though the X-Men were just around, to try to get in the way of mutants like Magneto who might cause problems for humans and mutants alike. But at the end of X2, the X-Men had a purpose as a team. The war was inevitable, and the X-Men were essentially the ones who were going to fight for human / mutant co-existance.
X-Men: The Last Stand touches upon all of the loose ends left open from the 2 films. This war that Magneto has predicted, that was pretty much made inevitable by William Stryker's actions. The fate of Jean Grey.
I won't go around talking about how this is an interconnected trilogy on the same calibur of Lord of the Rings... but these movies are still a trilogy in every sense of the word. These aren't just sequels that came out, to introduce new characters and stuff. These movies were brilliantly set up by Bryan Singer to actually connect to each other, and tell a larger story through interconnecting sub-plots. The movies pretty much work like this:
X-Men: Introduction. Magneto and his Brotherhood of Mutants make the first move against the humans, in response to the Mutant Registration Act. His actions are probably the first large scale mutant attack against humans, but because of Mystique's infiltration into the U.S. government by impersonating Senator Kelly, the Mutant Registration Act takes a hit.
X2: X-Men United: Rise in action. Col. William Stryker, who is anti-mutant, uses the Liberty Island incident as the spark towards his plan. He uses a form of mind control to have a mutant attempt to assassinate the President. And he uses that assassination attempt as a way to get authorization to attack Xavier's school, connecting the school, and "underground mutant training facility" to the assassination attempt. Of course, Stryker has plans of his own... getting the Cerebro technology so that he can make one of his own to destroy all mutants. The events at Alkali Lake are global scale, and are the first events to set off the all out conflict between humans and mutants.
X-Men: The Last Stand: Hostilities seem to be declining towards mutant-kind, as the new President has a Department of Mutant Affairs, a department which is headed by a mutant. But there are still some out there who want to get rid of the mutant "problem", and a cure is developed. Magneto sees this as the declaration of war from the humans, and builds his army to fight his war.
Overall, each film has a stand alone plot, yes, but each stand alone subplot connects each film together to tell one larger story. And I don't think you can have any of the movies without the others, and have a complete story.
I think we do have a complete story now, with the trilogy.