Infinity - Constantly regenerate reserve ammo for both your weapons.
Moonman - Gives you moon gravity!
Vampiric Investigator - Identifying bodies restores 15% of your health
Gambler - While above 50% health, deal 20% more damage. While below 50% health, take 40% more damage.
Big Bertha Repeater - Hold down the trigger to slowly increase the firerate
Laser module - A precise laser dealing extreme damage against heads. Regenerates energy when not in use.
Buckshot ammo Converter - Your rifle now shoots Buckshot.
Tranquilizer Bullets - Trough use of tranqlizer darts, these bullets slow animals (or humans) on hit.
Slightly reduces fire rate. Can only be applied to rifles or crowbars.
The Big Iron - Slow firing weapon of justice, hitting your target re-fills the clip. Missing causes a massive reload.
Stress Pump - The lower your health, the higher your gun’s stats. This gun is near worthless near full HP.
Plan C - C4 on a crowbar with a pressure sensor, The last option. Deals more damage the low HP you are.
Cupid bullets - Aim for the heart as these bullets only deal maximum damage to the body. Targets below 25% HP die and you heal for 75hp. Slightly faster Deploy speed.
Another Crowbar - You now hold two crowbars at once.
Leeching trigger - Base gun gains extra damage and accuracy with lifesteal, but uses your health as ammo.
tmtrainer module - Isaac and his mother lived alone in a small house on a hill.
Super Bullets - Bullets so powerful they propel you backwards. Force scales with firerate, damage and bullets. Can be applied to all guns.
Duck Gun - Happy birthday CCX!
EpicHugeFIx - Turns your Huge into an epic weapon, use with care!
Easter Bullets - This weapon fires exploding duck eggs instead of bullets, works on assault rifles
The Power Of God And Anime - May Crash The Server On Use
Feel free to add other exotics to this list.
(Dakka edit to put the hats in one section to avoid confusion)