There are 98/97 secrets in the Binding of Isaac. Here's a list of them, categorized.
Progression Secrets
Secrets you will unlock as you keep playing.
A Radioactive Spider: Complete the Basement.
Spelunker: Complete the Caves.
The Womb: Complete the Depths.
Something from the Future: Complete the Basement 25 times.
Something Cute: Complete the Caves 20 times.
Something Sticky: Complete the Depths 30 times.
Something Icky!: Complete the Womb / Utero 15 times.
Task Based Secrets
Secrets you will unlock upon completing specific tasks.
Mr. Mega: Destroy 10 tinted rocks, in total.
A Small Rock: Destroy 50 tinted rocks, in total.
The Bean: Destroy 50 piles of poop, in total.
Gamekid: Visit 10 Arcades.
Mom's Pill Bottle: Use a Blood Bank 20 times.
The Necronomicon: Use the XIII Death tarot card 4 times.
Mom's Eye: Collect Mom's Eye and either her Heels, Lipstick, Pad or Bra in one run.
The Common Cold: Collect either two of the following, in one run:
Growth Hormones, Roid Rages, Virus.
The Parasite: Collect two of either of the following, in one run:
Bob's Rotten Head, Dead Cat, Tammy's Head.
A Bandage: Defeat Famine, War, Pestilence and Death in one run, obtaining 4 Cubes.
Guppy's Hairball: Obtain three of the following items, and transform into Guppy:
Dead Cat, Guppy's Head, Guppy's Tail, Guppy's Paw.
The Pinking Shears: Die 100 times.
A Lump of Coal!?: Defeat Krampus.
A Halo:: Defeat Mom by using the Bible.
The Book of Sin: Defeat all the standard minibosses, over multiple playthroughs.
The Left Hand: Defeat Ultra Pride.
Characters and Character's Items
Secrets relating to characters or their items
Magdalene: Obtain 7 or more heart containers in one run.
Yum Heart: See: Magdalene.
Cain: Obtain 55 or more pennies in one run.
The Lucky Foot: See: Cain.
Eve: Make two Deals with the Devil in one run.
A Curse: See: Eve.
A Dead Bird: See: Eve.
Judas: Beat Mom's Heart for the first time.
The Book of Belial: See: Judas.
Samson: Skip on two Treasure Items and kill Mom.
???: Beat Mom's Heart (It Lives) for the 10th time.
The Poop: See: ???.
The D6: Beat Mom's Heart (It Lives) with ???.
Special Bosses and Related Items
Secrets related to unlockable bosses and their item drops.
The Harbingers: Defeat Mom once.
A Cube of Meat: See: The Harbingers.
The Book of Revelations: Defeat any of the four Horsemen of the Apocalypse, once.
Little Steve: Defeat Steven.
Little C.H.A.D.: Defeat C.H.A.D.
Little Gish: Defeat Gish.
Womb Completion Secrets
Secrets unlocked upon defeating the final boss in the Womb. Note: Some are under Characters and Character's Items.
A Noose: Defeat the final boss in the Womb for the second time.
The Nail: Defeat the final boss in the Womb for the third time.
A Quarter: Defeat the final boss in the Womb for the fourth time.
A Fetus in a Jar: Defeat the final boss in the Womb for the fifth time.
Everything is Terrible!!!: Defeat the final boss in the Womb for the sixth time.
The Wafer: Defeat the final boss in the Womb for the seventh time.
Money=Power: Defeat the final boss in the Womb for the eighth time.
It Lives!: Defeat the final boss in the Womb for the ninth time.
A Cross: Defeat the final boss in the Womb with Maggy.
A Bag of Pennies: Defeat the final boss in the Womb with Cain.
A Robo-Baby!: Defeat the final boss in the Womb with Judas.
The Razor: Defeat the final boss in the Womb as Eve.
Blood Lust: Defeat the final boss in the Womb as Samson.
Sheol Completion Secrets
Secrets unlocked upon defeating the final boss in Sheol.
Mom's Knife: Defeat the final boss in Sheol with Isaac.
Guardian Angel: Defeat the final boss in Sheol with Maggy.
The Monster Manual: Defeat the final boss in Sheol with Judas.
Blood Rights: Defeat the final boss in Sheol with Samson.
A Demon Baby: Defeat the final boss in Sheol with Eve.
A Bag of Bombs: Defeat the final boss in Sheol with Cain.
A Forget Me Now: Defeat the final boss in Sheol with ???.
Cathedral Completion Secrets
Secrets unlocked upon defeating the final boss in the Cathedral.
The Polaroid: Defeat the final boss of the Cathedral six times in total
The D20: Defeat the final boss of the Cathedral with Isaac.
The Crucifix: Defeat the final boss of the Cathedral with Maggy.
Curved Horn: Defeat the final boss of the Cathedral with Judas.
Bloody Penny: Defeat the final boss of the Cathedral with Samson.
Sacrificial Knife: Defeat the final boss of the Cathedral with Eve.
Abel: Defeat the final boss of the Cathedral with Cain.
Rainbow Baby: Defeat the final boss of the Cathedral with ???.
Chest Completion Secrets
Secrets unlocked upon defeating the final boss of the game, in the Chest.
Maggy's Faith: Defeat the final boss with Maggy.
Judas' Tongue: Defeat the final boss with Judas.
Samson's Lock: Defeat the final boss with Samson.
???'s Soul: Defeat the final boss with Eve.
Cain's Eye: Defeat the final boss with Cain.
Eve's Bird Foot: Defeat the final boss with ???.
Challenge Secrets
Secrets unlocked by completing the challenges.
The Candle: Complete Challenge 1.
Lucky Toe!: Complete Challenge 2.
Burnt Penny: Complete Challenge 3.
Guppy's Tail: Complete Challenge 4.
A Fish Head: Complete Challenge 5.
Mega Fetus: Complete Challenge 6.
Super Fan: Complete Challenge 7.
Spider Butt: Complete Challenge 8.
Counterfeit coin: Complete Challenge 9.
The Egg Sack: Complete Challenge 10.
No Damage Secrets
Secrets unlocked by taking no damage on their respective floors. Note: Every floor can be replaced with their alternate, ex: Basement, Cellar.
Basement Boy: Complete the Basement I and II without taking any damage.
Spelunker Boy: Complete the Caves I and II without taking any damage.
Dark Boy: Complete the Depths I and II without taking any damage.
Mama's Boy: Complete the Womb I and II without taking any damage.
Final Secrets
You must also pick up all the items atleast once.
Golden God: Unlock all the vanilla game achievements / secrets and items.
Platinum God: Unlock all the achievements / secrets and items.
See the Achievements section for explanation.
