Gaara from Naruto usually covers himself with sand armor that looks like his own skin when his sand shield is not enough. He can also channel Shukaku and assume its form. Funnily enough the 'armor' aspect is negated in a full channeling as he has to remain exposed on Shukaku's forehead.
Kakuzu also had an Earth Release technique which turns his skin as hard as steel and also greatly increased his physical strength.
Kidomaru can produce spider silk from his body, including a special kind which turns hard as steel when it touches air, and in a pinch he can cover his body with it to form a sort of armor.
When the 9 tailed fox manifests, it surrounds Naruto with chakra which damages his body but protects against enemy attacks.
The Raikage can use his lightning aura to create lightning shields, among other things.
In YuYu Hakusho, there is Risho, the demon ninja with power over rock that Kuwabara fought in the Dark Tournament. His main attack was to create a rock armor then tackle his opponent.
And for the armor-out-of-thin-air example, we have Sensui, who can use his Holy Light Energy to create two special sets of armor.
In Toriko, Zebra can create "sound armor'' around a person to protect them from harm.
Coco can create "poison armor" for himself, complete with a sword.
Gajeel Redfox from Fairy Tail might count, since he has the ability to instantly transform his skin onto steel armor. This coincides with Extra Ore Dinary as well - his transformed state is the page image for the trope.
Iceman could create a coating of ice armor on his body.
Magneto's suit works like this in some adaptations - Though it sure looks manufactured rather than improvised, he can form one from whatever metal is available. At one point when He's Just Hiding the base where he was supposed to have died is found and his suit is still there - upright despite being empty and (judging by the neck line) about half an inch thick.
A minor Great Lakes Avengers character is named Debris, and she can control junk to create armor in the form of a giant junk monster around herself.
Dungeons & Dragons codified the stoneskin and ironskin spells. The games also include the spell fireshield, which doesn't so much protect as it does exact pain on anyone who strikes the person "protected" by it.
Flaming Armor and Lightning Armor from GURPS: Magic.
Forgotten Realms has spell "Rainbow Shield" allowing to use any attack spell this way (Fireball to more or less fire shield, Lightning bolt to lightning shield, etc).
Exalted: Some Charms and Martial Arts (especially Dragon-Blooded ones) can create them (Fire-Aspects are appropriately Wreathed in Flames). Solar Exalted can create shiny awesome armor made of sunlight, while Abyssal ones can create similar armor made of darkness.
Changeling: The Lost has the Contract of Elements, which has a clause (read: sub-power) allowing the changeling to wreath themselves in an armor of whatever element he bought the Contract in. Not only does it protect against attacks, it damages anyone who tries to touch him.
Kratos in the first God of War had Wrath of the Gods, which grants him a full set of Greek armor made of lightning.
There are a bunch of powersets in Cityof Heroes which allow for elemental armors, including Stone, Fire and Ice, as well as the more exotic (Dark, Energy and Electricity). Each powerset has multiple types of armor with different effects; for example, Frozen Armor protects against physical damage, Glacial Armor protects against energy, and Wet Ice helps against status effects. In the old days, you could only have one active at a time; that quickly changed.