The Other Darrin: Just take a look at the character sheet. Practically every character to appear in more than one game has had this happen at some point or another. Part of it can be attributed to the fact that all of the gods were completely redesigned between the first and second game, other times it's just good old-fashioned recasting.
Self-Deprecation: Meta-example. Series creator David Jaffe has stated that he finds the games' combat to be shallow compared to other games in the genre, and that he would have made the series a little differently if it were a new IP today. Possibly downplayed, since he never expressed explicit dissatisfaction with the mechanics, and even went on record to bluntly say he is not decrying the games themselves.
There was going to be a movie adaptation directed by Bret Ratner.
The original plan for the series was for Kratos to travel around the world after the destruction of the Greek pantheon, meet his counterpart of other mythologies, and repeat the process of destruction over and over. Finally ending with traveling alongside his two surviving counterparts, and following a shining star in the night sky to the birth of child in a manger...