Strong film franchises need strong, returning characters just as much as they need a good enough story and the money to get them to the screen. They're the familiar faces audiences depend upon to be their emotional surrogates and their idols: we can't experience anything as audiences quite as well as if they're happening to people we care about, after all. Or care enough to dislike, at the very least.
So it always comes as a bit of a surprise when movie sequels simply dump establish characters for no apparently logical reason. And it's even worse when the excuse they give simply doesn't work. At least give them a good send-off - it's the least they deserve!
Tom Hagen was as big a part of the Corleon family as anyone bearing that surname: he was consigliere and stood in for Michael Corleone as the Don when someone tried to assassinate him. By rights, he should have been a presence all the way through the trilogy, but it wasn't to be as he didn't return for the third installment.
Why He Was Written Out
It was all down to money. Robert Duvall turned down $1 million for the threequel, demanding that his salary matched Al Pacino's $5 million instead. The studio balked at the idea and simply dropped him, despite Francis Ford Coppola expressing regrets later.
How He Was Written Out
Ironically, the third movie would have dealt with Hagen and Michael clashing, developing a deleted subplot from the second movie that saw Hagen and Sandra Corleone (Sonny's widow) shacking up and Michael blackmailing him into remaining loyal despite Sandra's urging to leave the family.
But when Duvall's contract demands got in the way, Coppola simply wrote Hagen out, dismissively killing him off between the movies and robbing us of an intriguing narrative thread.