By fulfilling certain conditions, you'll receive a notification that a new item (or items) have been unlocked. Any items unlocked this way have a chance of randomly appearing during subsequent runs, such as in shops or as rewards for beating bosses.

Item	How to unlock
A Quarter	Defeat Mom's Heart for the eighth time.
Ball of Bandages	Defeat Mom for the first time.
Black Candle	Donate 150 Coins to the Donations Box.
Blue Map	Donate 10 Coins to the Donations Box.
Book of Revelations	Defeat a Harbinger for the first time.
Cube of Meat	Defeat Mom for the first time.
Dr. Fetus	Defeat Mom's Heart for the ninth time.
Experimental Treatment	Defeat Mom's Heart for the seventh time.
Head of Krampus	Defeat Krampus for the first time.
Ipecac	Defeat Mom's Heart for the sixth time.
Little C.H.A.D.	Defeat C.H.A.D. for the first time.
Little Chubby	Complete The Caves (or equivalent level) for the first time.
Little Gish	Defeat Gish for the first time.
Mom's Knife	Defeat Satan as Isaac.
Monstro's Tooth	Complete The Basement (or equivalent level) for the first time.
Razor Blade	Defeat Satan as Eve.
Red Candle	Donate 400 Coins to the Donations Box.
Rubber Cement	Defeat Mom's Heart for the second time.
The Book of Sin	Defeat each one of the Deadly Sin enemies.
The Halo	Defeat either Mom or Mom's Heart by activating The Bible.
There's Options	Donate 50 Coins to the Donations Box.
Transcendence	Defeat Mom's Heart for the third time.
Wire Coat Hanger	Defeat Mom's Heart for the fourth time.