How much innovation do we as fans allow for in game series?

By this I mean, as a gamer do you love to see games being reinvented throughout a series? Do you love innovative game mechanics and character development that maybe differs drastically from the first game in a series? Or even, as a fan are you willing to let game makers try new things with series or games you've grown attached to?

Or do we shy away from and become intolerant of games that don't follow a specific pattern or stray from our expectations?

And what game series have you seen change drastically over time?