There's never been a time I was not sure I was totally indispensable to the company... right up to the moment I got fired.
I've been at my company seventeen years and had an interview last week. If they offer it, I'll take it. I think my company would describe be as indispensable, but the problem is I don't discuss my frustrations with the company, I discuss them with three people. Those are the people who could take some action. When I leave, those are the three people who will shrug, go through a hiring process, and deflect work that can't get done without me. The company will keep going.
When it eventually comes time for me to resign, I'm curious what the reaction will be. The CEO knows who I am and the senior VP knows me fairly well (though he's a phenomenal people person), but not enough to say "are you happy here," and not enough to review our employee surveys results (which are poor for my group) or if he is, he doesn't care. I think a lot of people will be surprised because they assume high quality enthusiastic work means I'm happy with work.
A different long term employee left recently under undisclosed terms. I had assumed it was something medical e.g. a very sick loved one, but I heard she landed a new job immediately. She had more time than me and is probably in her 50s.