X-Men: The Official Game takes place between the final two films and acts as a bridge between the events at Alkali Lake in the second movie to the events at Alkali Lake at the beginning of the third movie. So where does this game take place? Why, Alkali Lake, of course!
Wolverine, Colossus, Iceman and Nightcrawler travel back to the place of Jean Grey's death in order to look for the stolen Cerebro components that Colonel Stryker used in the second "X-Men" movie. The band of mutants quickly discover that the facility is not as dead as they once believed as the workers start preparing the damaged base and try to bring it back to running condition. So now, the four mutants will go through level after level of defeating grunts and mutants alike in order to stop the facility once and for all, as well as retrieve the missing Cerebro parts.
As you fight through the factory, you will meet up with villians like Pyro and Sabertooth, and typically you will be forced to play as only one or two characters in these circumstances. This is to allow for some of the more classic battles like Wolverine versus Sabertooth or Iceman versus Pyro, but for the most part, all four of the characters are at your disposal.
Since you are playing as all four X-Men, you can switch between them at will in order to use each one's special abilities. At least that is the theory, and while each one does have some uniqueness to them and you can switch between each character, the characters themselves are just too similar to really make any difference.
Levels are straightforward and don't really require a lot of effort to get past. You run from one side of the screen to the other killing anything that moves until you find the exit, then you do it again. The worst part of this game is that there is nothing to break up the monotony.