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Do you get a proficiency bonus to AC when wearing armor you are proficient with?

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No. Proficiency only allows you to don that type of armor without suffering disadvantage on all rolls involving strength or dexterity. In that way it is mechanically identical to 3.5 armor proficiency, removing a penalty associated to doning an armor you are not proficient with, but serving to no other purpose, other than maybe being a requirement for certain feats.

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  • \$\begingroup\$ With the Bounded Accuracy ( wizards.com/dnd/article.aspx?x=dnd/4ll/20120604) WOTC implemented in D&D Next, you AC doesn't goes up as you level up to ensure that you feel like you really get better at hitting things. The progression on dodging is included in your HP, because it's not because you were Hit (gameply term) that you were actually hit (roleplay term). A successful attack, can mean that the attack was close and you made a last second dodge and was barely bruised. \$\endgroup\$
    – Groumy
    Sep 25, 2013 at 13:24
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PCs get to improve their AC by being able to buy more expensive armor/raising their Dex mod by 2 and it is likely that someone who cares about their AC finds approximately a +2 or the equivalent benefit to AC over the course of 20 levels via magic items.

Monsters improve their to-hit by the equivalent of +6 over 20 levels(page 274 of DMG). So a CR 20 monster has a +2 advantage swinging at a 20th level PC compared to a CR 1 monster swinging at a 1st level PC. Oddly enough, given that CR 20 monsters have a +7 AC advantage over a CR 1 monster and PCs are likely to find a +3 weapon over that time period(page 133 of DMG's typical treasure), and raise stats by +2 modifier+get +4 proficiency for a total of +9...

i.e. from levels 1-20, you should expect that both Monsters and PCs hit more often by a total of +2.

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