I don't know about characters. I go either by whole books or by incidents in the books. Like so:
1) One of my all-time favorite Dr. Seuss books is also one of his least-known. The King's Stilts. Gotta love those nizzards and Patrol Cats!
2) I loved I Had Trouble Getting to Solla Sollew. As an adult, I noticed a subtle joke in there that I completely missed when I was a child. One of the boy's troubles is he is stuck running though a tunnel with 500 birds "going all the wrong way." The joke is that THEY aren't going the wrong way, HE is! Out of all the troubles he experiences, that one is entirely his own fault.
3) Still on Solla Sollew, I can recite the bus stop scene by heart.
Well, the bus stop was there. That part was just fine.
But next to the bus stop was a small sign
Saying "Notice to passengers using our line
We regret to inform you our driver, Butch Myers,
Ran over four nails and has punctured all tires.
So, until further notice, the 5:32
Cannot possibly take you to Solla Sollew.
But we wish you a most pleasant journey by feet.
(Signed) Bus line president, Horace P. Sweet."
So I went on by feet, thanks to Horace P. Sweet.
And that Horace P. Sweet almost ruined my feet!
4) The scene with the pants with nobody inside 'em scared me out of my wits when I was little. The funny thing is, even though I was old enough to read for myself, the title of the story (and hence the message) went completely by me — "What Was I Scared Of?"