James Bond
No character is more able to survive actor replacements than James Bond. Perhaps that’s because “character” might be too strong a word for Bond. He’s not exactly the meatiest of roles: really, “British” and “Looks good in a tux” are about all you need in the special skills sections of your resume to land this role, given that sexism isn't even a pre-requisite any more.
The favourite Bond of The Quietus is the original radio incarnation played by Bob Holness.