In my post What Happens After Happily Ever After? I mention that I often find myself wondering and imagining what happens after the credits roll.
House's final episode pulled something fairly close to a happily ever after. House faked his own death to avoid jail time and rode off on a motorcycle with his best friend, Wilson, who has five months to live.
Naturally I am unsatisfied with this conclusion. Not in an annoyed-with-the-series way, since they had to end it, they did well with the ending.
But here's my theory on what would happen to the characters. We see that Chase takes over as Head of Diagnostics, Foreman continues as Dean of Medicine, Cameron as the head of the ER. Those stories I see continuing more or less as is. They take what they learned from House and are better, more efficient doctors. It's a good legacy.
But what happens to House and Wilson? In their final on-screen exchange, Wilson tries to talk about what he wants when his cancer begins to get bad. House stops him, saying "Cancer is boring."
House has faked his own death. He can't be a doctor any more. No more diagnostic puzzles to solve. He's given up the one thing he cares most passionately about in order to be with his best friend during the last few months of Wilson's life. Not bad for a self-professed ass whose selfish actions have defined the series.
I don't think it could last.
House has never been able to resist a puzzle when he saw it. Even when he knew it would cost him his freedom (at the beginning of the season when he was in jail) or his health (when his psychologist told him he absolutely had to stay away from medicine and the hospital to avoid relapsing into drugs), the puzzle was always more important. I could see a potential reunion TV movie, three to five years from now, where rumours of miraculous diagnoses lead House's old team back to him. He won't be able to resist revealing himself.
They wouldn't even have to leave Robert Sean Leonard off the cast list. House has had many hallucinations acting for his subconscious mind. Although Wilson would be dead, a hallucinatory Wilson would probably continue to provide advice and warnings. So House wouldn't be entirely without his best friend.
I'm not sure where the story would go from there, but I think those two facets are inevitable if House survives past Wilson's death. He wouldn't be able to resist the medical puzzles he would run across and he would continue to hallucinate Wilson.
I say "if House survives" because I don't think that part is guaranteed. House is self-destructive and prone to dramatic, simple solutions to his pain. I would guess there would be a significant chance House would commit suicide, deliberately or subconsciously, when Wilson finally died.
Those are the two paths I see stretching out after close to eight years of watching these particular characters. I don't know if anyone will professionally revisit the world of House, although I'm sure fanfiction will continue to churn.
For myself, I'm content to wish them all well on their future fictional paths. They entertained and made us think, laugh and cry. You can't ask any more than that.