If I have a character of mine die, my favorite bit is to have my new character have some relation to the old character. Now, most would use this to replace a character with a stand-in. “What do you know, my character had a brother of the same stats and class!”

But I find that too boring. I prefer to go with an entirely new class when a character dies or otherwise must be replaced. My favorite bit is to have the new character be out for revenge against the old one. This has in the past resulted in a new character fighting a pitched battle with my old one.