I was poking around answering for this question about the highest AC possible for a sorcerer and noticed something odd.
It doesn't seem to be possible except in the case of the Barbarian to naturally get your AC over 20 without the use of magic items.
Is there a way that I'm missing or is this a relatively hard and fast rule (with the noted exception of the Barbarian).
The Barbarian's exception lies in the fact that he gets to add Dex and Con to his AC, and his Level 20 capstone is a +4 bonus to CON (to a max of 24, which I'll assume here), which gives him a potential AC of 24 (Dex 5, Con 7, shield +2).
(Note: I'm looking for permanent solutions; if you want to delve into spells, they should have duration similar to mage armor and not require concentration.)