I personally don't dislike the idea of making a fourth part, because as the Godfather wikipedia says, Coppola wanted to conclude it with Vincent being hunted down and killed by the police. In fact, it would be interesting to see the law enforcement finally DO SOMETHING about the mafia, in the 3 films that have been made they are just almost non-existent dummies.
That's why a fourth part should end with Vincent being send to prison for life, instead of being killed. He wanted "in", then he has to pay the price for it.
