Guardian - perhaps even the one shown at the start/end of TPS?
Crazy Earl - I have no idea what his abilities would be like.
Moxxi - obviously with good health regen abilities
Marcus - someone mentioned him before somewhere
Some sort of superhero like someone from Marvel or DC comics. A stretchy arm guy for example.
Claptrap Res’d Roland
Claptrap Res’d Steele
Some Half man half skag abomination (or pick another wildlife from Pandora)
Someone with a pet Thresher action skill
More ideas?
These are all terrible ideas. And that stretchy arm guy is Mr. Fantastic Reed Richards, I hate “stretchy arm guy.” I know I’m not the only one whom wants something completely new for Borderlands 3.
A racist hot dog.
I love the thresher pet idea. Badass fire, elemental tree. Wormhole, shotgun and fire rate. Landscape, slings spikes at enemies, also spike damage to melee. Capstone: mini Terra.
Her skill would be flooding everything and riding on fish with crazy music happening and throwing barrels. 
…and then teleport to Nina for some heals.
I think it would be interesting to have a character that’s more co-op minded. The last bad guy this character killed, he/she takes on their offensive and defensive abilities to a small degree as an action skill. Let’s say the character kills a nomad with a shield, the character can digistruct a similar shield and now has better defensive capabilities until he/she kills something else or he/she could choose not to kill anything else and just use the shield to help protect the team.
If he/she killed the Bosun or Deadlift, he/she could now fire off shock attacks until the next kill that overrides this offensive attack. So it’s very tactical and you need to chose who to kill very carefully.
This guy knows what needs to be in the game.
Dr. Ted gets my vote too.
A playable Goliath could be funny.
Craziest? OP - you titled your thread “Craziest” and all of your ideas, while pretty decent are not close to crazy. How about a playable vending machine - in co-op your partners could buy ammo off of you and your Action Skill uses whichever Item of the Day is currently active in you and fires it as a secondary weapon (and a game changer is to hold the melee button to drop it so you can pick it up if it is something you want to keep).
Crazy? How about a playable Pet that summons a vault hunter to fight for it, each of your skill trees is dedicated to one of three summonable VHs and the chances of summoning a particular one depends on the amount of points you put in their tree.
Hmm, these are strange but all too plausable. I guess I can’t do crazy either. Crazy might be a playable burrito that goes around making scalding hot salsa puddles of death. Maybe “Craziest” should not have been in the thread title.
I like that.
His skill could be related to his giant head…notice how big it looks through that slot? Always cracks us up.
A headbutt melee override? Yes please! Maybe it could be an explosive headbutt??!
Ginger Rugby vaulthunter.
If were to think of a crazy person for Pandora… Hmm…
Joe the Christian
Action skill-
Religious Teachings. He will pull out his bible and start preaching out loud, which makes enemy’s hostile to each other, increases movement speed and adds health regen ( with a upgrade that allows you to throw holy water at enemy’s, called "power of Christ).
Hope I didn’t offend anyone
A playable BOGAN!
The dialogue alone would turn the air blue!
His/her skin would be tracky dacks, UGG boots and a T’shirt with a pack of smokes rolled up into the sleeve.
Head skin would be a mullet.
HIS name would have to end in “O” such as Jacko, Robbo, Dicko etc
HER name would have to be Raelene, Shaelene, Darlene,Charlene or Sheila.