"Armor" in Borderlands can be broken down into one of two schools of thought.
Statistics and Visuals. It's all represented, just probably not in the traditional sense you're thinking of.
We have a very robust system for upgrading your character in ways that are not weapons. You can upgrade:
-Shields
-Class Mod
-Artifacts
All of these added together provide the same ability to customize your character as a traditional RPG, albeit in a slightly simplified matter. A shield is basically what keeps you alive, but with thousands upon thousands of them around, you're sure to find some that do really interesting things (faster recharge, higher capacity, do damage to enemies, light **** on fire, make you breakfast, etc.)
In addition there are class mods which do all matter of crazy things. Class mods are specific to Hunter, Siren, Besersker, Soldier, and can affect any number of things. Some buff your existing skill tree stats, some increase individual skills as well as well as Co-Op skills (i.e. stand next to Mordecai and your accuracy goes way up!) Some do crazy stuff like multiply the number of bullets you fire each time you fire your gun... the list goes on. I'm just listing off the crap I've seen-- and there's no way I've seen all of it.
Artifacts are another type of collectible gear. These are rare, and they can have really insane effects. The one I have on my Bloodwing right now actually blows people up on contact... it's crazy. And hilarious. And everyone loves a bird that can blow people up. That's the only one I'll spoil... Artifacts are the super happiest drop you'll find in Borderlands.
And as for visuals. We separated the visual customizations of the characters from the gear upgrades to allow people to look how they want without affecting their gear. Like in some games... you end up looking like a total dork just to get the stats you need. Not so in Borderlands. The characters can be customized and re-customized at any New-U station around Pandora.