The Evil Dead series. The first installment was a straight up horror movie. The second was a horror comedy. Third was a fantasy comedy.
Beat me to it. That's probably the clearest example. The second movie is virtually a remake of the first except that it's a comedy. The third is completely different that it really isn't even horror.
While they are both action movies, the second one builds up the plot a lot more and has a very different feel to it. Not that I don't like it, they're both good movies. But they have very different feels.
I really like the difference in tone between the two movies. It's part of the reason I'm glad it was split up rather than stayed as one movie. It works well as two parts. That being said, while the tone changes dramatically, I'm not sure I would say it switches genres (especially since there are many subgenres sprinkled throughout anyway).