In TP, he has chainmail. Apparently he also has it in Skyward Sword. If you pay attention while playing A Link to the Past, some of the upgrades you get in the latter dungeons are "mail" "Blue mail," "Red mail."
In the earliest games, LoZ and AoL, there's a magical counterpart in the magic rings that increase defense (LoZ) and the Shield Spell (AoL). The tunic changes color - no indication of armor or mail there, but the magic suffices.
In OoT, MM, Oracles and WW - the poor kid's practically naked! Well, he has clothing, but no battle-protection. Limited magic-eating spells like Nayru's Love and WW's "Magic Armor" are all-proof armor that suffice for short periods, but aren't like a regular general protection like mail.
I was happy to see Link in chainmail in TP - it's like "Yeah, Nintendo, he NEEDS that!"
It's still limited, though, but think about it - if Link is wearing light armor (chainmail shirt) or is just in tights and tunic without armor, he has a speed/agility/movement advantage, does he not? Knight's armor is clunky. And you can't go to the bathroom in it either, unless you go to the bathroom *in* it (thank you, History Channel!) All of the armored foes in the games are pretty clunky (with the exception of Darknuts in the original LoZ, who were speedy... the arfijdigd^&%%%!!!ing things! ) In the 3-D games especially, light or no-armor Link has a definitive speed and manuverability advantage.
Perhaps his Courage causes him to eschew lots of protective armor in favor of the speed/manuverability advantage, despite the risk.