According to SciFi Wire through Coming Soon, the Chairperson of Sony’s Motion Picture Group is on for six Spiderman movies:
“I’ve heard Amy Pascal say she wants to make six Spider-Man pictures,” Raimi said in an interview at the Saturn Awards in Los Angeles. “So I think she’s a woman of her word. And if she says there’ll be six, there’ll be six. … If they were to ask me, and if I felt as passionate as I feel now about the character and had this great hunger and desire to tell the story, which I really do now, you couldn’t keep me away from it.”
Huge speculation, and as we know from many of the movie rumours (especially Bond) it could be Raimi trying to position himself for a job, but I seriously doubt that. It does sound like there has been speculation on the back of the success of the first two movies, but the success of another three depends on retaining Raimi or finding a Director who is as much a fan as a driven Director. Would you like to see another three movies after this one?