Well from earlier analysis of this thread:
http://www.enworld.org/forum/showthread.php?475208-Highest-Possible-5E-AC
I can get to AC: 36 with a Level 20 Barbarian and lots of magic items and spells...
Barbarian at level 20 gets Primal Might (+4 STR and CON, raises the cap to 24), so can have 24 CON.
So Unarmored Defence with DEX 20 (+5), CON 24 (+7) = 10+5+7 = AC:22 base
Using a +3 magical shield
+2 from shield,
+3 from it being a Magic Shield +3. (+3 shield is a very rare item does not require attunement)
= AC: 27.
As the +3 Shield doesn't require attunement.
Then:
Ioun Stone of Protection- +1 AC (Rare item that requires attunement)
Cloak of Protection +1 AC (Uncommon item that requires attunement)
Ring of Protection +1 AC (Rare item that requires attunement)
= +3 AC
= AC:30 (AC 35 in 3/4 cover)
If you replace one of the items with a Defender (Legendary item that requires attunment) and use it's full bonus then it goes to +3, +1, +1
= AC: 32 (AC: 37 in 3/4 cover)
Contrary to initial assumptions, there are no enchantment bonus or similar anti-stacking mechanic. I believe the semi-official tweets confirm it's ok to stack AC from magic items if the DM lets you get hold of them.
Then someone casts Shield of Faith on them for +2 more AC. And SOMEONE ELSE casts Haste on them (they're both concentration spells) for another +2 AC
= AC:36, (AC:41 in 3/4 Cover) with Shield of Faith and Haste.
Defensive Duelist (When you are wielding a finesse weapon with which you are proficient and another creature hits you with an a melee attack, you can use your reaction to add your proficiency bonus to your AC for that attack, potentially causing the Attack to miss you. Then as a Reaction after (somehow) being hit by a melee, can increase AC against that single hit by Proficiency bonus: so +6 at levels 17+ putting it at:
= AC: 42 (47 in 3/4 Cover.)
(Shield spell also uses your reaction and grants +5 but lasts until the end of your turn and it's just melee. +6 AC due to proficiency.)