Well I am guessing that number 3 will resolve Peter/Harry's relationship, which means that the first three is a loose trilogy around the relationship between Peter/Harry and also MJ.
So if 4,5 and 6, came up with either three decent individual stories, or a trilogy with Peter and a hgue villain, then it could work. I trust Sam Raimi to only do these if he is still interested (and therefore have a better chance of good films).
I do too. From what I've seen, heard, and read about him, he's trying to remain as true to the comics as feasibly possible and making a quality movie. I think he'll look to only make a film with a strong script.
This is all assuming he is there for the fourth through sixth ones.
Also, I think that as long as Stan Lee is alive and has a hand in the movies he won't let the film series deteriorate ala Batman.