I know everyone is most likely going to say the feet of the character because of it being that way IRL as the feet do indeed have the most nerve endings

Least ticklish has to be Timon of the Timon & Pumbaa cartoon series.

He's actually involved in a brief tickle scene (VERY brief) where his only reaction is a bored expression. It's in the episode The Man From J.U.N.G.L.E.

Most ticklish though? Hmmm...

Hard to say, though Bonkers the Bobcat having some pretty extreme and silly reactions to even the slightest of tickling could make him a candidate. However, as a character who is explicitly a cartoon in a "normal" world, he's kinda *required* to have exaggerated reactions to everything.

There's also Glugzilla from the older Ducktales series where a brief armpit tickle (in just one of his four armpits!) leads to him laughing uncontrollably for several seconds as he lets go of the city he's trying to hold up.

(Tickle scene here: https://www.youtube.com/watch?v=YJTiBloV_9M )

Danger Mouse and Injun Joe had the biggest reactions that I can think of, at the moment. Though one medical lead on his side was enough to get Scooby giggling.

Unfortunately I don't like my answer.
Because the most ticklish characters are obviously the ones who can feel feathers through clothing. Which sucks and I hate it XD This guy has fucking SHOES on: https://www.youtube.com/watch?v=tI2YR3uM2Ag
Tired right now, so not really coming up with scenes of least ticklish. I remember one from the US Acres cartoon but I can't find it online right now.

Now I'm depressed XD

Most would go to the Fox from Redwall or Michelangelo from TMNT, there's a scene where he's tickled with a giant energy feather but I can't seem to find the clip.