Not including TVHM, I got the flame of the firehawk shield, a barking volcano, and a bee shield (a low level one from a vending machine). Of all of those items, the firehawk shield lasted me the longest.
Yikes, I feel spoiled with my luck. I've randomly come across 13 on my PT 1 with Axton. And because it was PT 1, they were largely useless as they wore out quickly as I levelled up, and later I was already levels above when I found them.
-Hornet (Knuckledragger) -KerBlaster (Midgemong) -Thunderball Fists (Flynt) -Infinity (2 from completely random Doc Mercy detours) -Rolling Thunder (ammo vending machine) -Gub (Laney) -Legendary Berserker mod (Holy Spirits medic vending machine) -Legendary Soldier mod (very same vending machine as above, subsequent visit) -Deliverance (Tumbaa) -Mongol (gun vending machine) -Cradle (Henry, 3 or 4 while farming for the Dapper Gent) -Veruc (Overlook gun vending machine while selling unwanted Henry drops) -B-word (Bunker, technically 'farmed' but was trying for a purple relic for the Decked Out achievement)
Out of the weapons, I only really used the Hornet, because it was so early in the game and the corrosive was handy and otherwise unavailable until you found such weapons in the mid teen levels. I twinked the Deliverance and Veruc to Gaige and so those saw some good use, too.
And with other characters:
Maya -Gunerang (Sanctuary slots with Maya, only character to get 3 vault symbols)
Gaige: -Volcano (gun vending machine) -Fabled Tortoise (Blue.. running through Caustic Caverns for the Open Wide and Crystalisk challenges) -Impaler (medic vending machine in PT 2) -also saw a Pyrophobia really early in a Sanctuary gun vending machine that I couldn't afford to buy and maintain.. no one was selling rocket ammo yet. --- It's raining luggage and babies and limbs and Daddy doesn't come home.