I've only just started playing so almost all of my character concepts I haven't gotten to play yet. So I'll tell you about the one I think I am least likely to ever run because it is a little goofy, requires a willing DM and kinda needs to be in a campaign that goes to very high level to get a satisfying ending which I know is rare.

There is a powerful and traditionally evil necromancer experimenting with new spells. He wants more intelligent servants that can assist him with research. Undead computers essentially. But when casting the latest version of his spell, he ends up animating his own skeleton. They fight for control and the skeleton of course wins. It is intelligent and starts to teach itself magic. It will become a necromancer as well but a true neutral. It wants to find a way to separate/ gain its own body. The original necromancer just wants to destroy it.

Mechanically it would just play as some form of elf. It doesn't need to eat or breathe technically but the wizard it is inside of does and it is is its own best interest to keep the wizard alive until it can gain a full body of its own. Its better to appear as wizard than a skeleton after all. Sometimes it will interrogate the wizard for knowledge, appearing to beat himself up. This will just be a fluffy way of explaining where the spells he gains on level up come from and how the sage background feature would work.

Sometimes a stranger will recognise him as the evil necromancer, up to the DM.

I like it a lot but I know it requires a bit of a flexible interpretation of "undead". The reason it needs a campaign that goes high level is the best way I can think of to accomplish its goal is a slightly creative interpretation of the clone spell. Unless I could work with the DM to come up with a custom and more attainable solution. Another reason I'll probably never run it is party compatibility. It won't be evil or anything but I don't see the typical paladin or cleric being cool with it.