One of the endings: Isaac dresses as Dr. Fetus from Super Meat Boy, complete with the stage title theme from that game. Unsurprisingly, the ending gives you the Fetus in a Jar powerup. There's also a power-up called "Doctor's Remote," which is another reference to the character in question.
C.H.A.D. can appear as an alternate version of Chub.
Meat Boy himself appears as a familiar when you collect Cubes of Meat, and Wrath of the Lamb adds a "SMB Super Fan" circular saw item that transforms the player character into a Meat Boy lookalike.
The Larry Jr. boss is presumably related in some way to Larries' Lament from the second-to-last world of Super Meat Boy - possibly meant to be the miniature versions of them that pop out of their head in the ending.
Rebirth has Bandage Girl appear as a familiar when you collect balls of bandages.
A more meta one: the achievements for completing floors without getting hit in this game follow a scheme of "____ Boy", which is the same pattern that the achievements for completing worlds without dying in Super Meat Boy followed.
One of the new bosses introduced in Afterbirth is Little Horn, not to be confused with Super Meat Boy'sLittle Horn.
A number of internet meme faces make an appearance, particularly the Forever Alone and Troll Face, with the latter appearing on bombs which are ready to go off. And let's not forget Shoop-Da-Woop!, which is a charged laser weapon. There is also an enemy type with a distinctive trollface that will split in half upon receiving enough damage, and the duplicates will split further into even smaller copies, demonstrating the spirit, as well as appearance of the trollface. In its smallest form, it becomes a Pokerface. Occasionally, the corpse sitting in one of the secret rooms will be sporting the "forever alone" face as well.
One enemy type is the same species as Gish. Gish himself can appear as a boss as well, and drops a baby version of himself (a familiar whose shots slow enemies) when defeated.
The "Pills Here!" message after picking up a pill is a shout out to Left 4 Dead.
One effect that pills can give you is "Balls Of Steel," which gives you 2 soul hearts.
The null effect for pills is "I found pills!", with the fake effect "And ate them". This is likely a throwback to an early LOLCat macro.
The "My Little Unicorn" item seems to be a shout out to My Little Pony.
The "Technology" upgrade is a clear reference to the Borg.
One of the new items in Wrath of the Lamb is the Notched Axe, a pickaxe that can be used to break rocks. This is a double reference, shouting out to the Notched Pickaxe from The Elder Scrolls V: Skyrim, which was itself a reference to Minecraft and its creator, Notch.
The Chemical Peel item will give you a Harvey Dent makeover.
An item named "Telepathy for Dummies," looking exactly like any "For Dummies" book would look like.
One of the messages you can get from the Fortune Teller is "Look to La Luna." This was the clue on how to find Reptile in the original Mortal Kombat game. Two others, "MARRY AND REPRODUCE" and "STAY ASLEEP", reference They Live. It's also possible to get "I feel asleep!!"
Subverted in the case of Gluttony. A lot of fans think that his appearance and the blood-laser that shoots from the stomach are references to Fullmetal Alchemist; HOWEVER, Edmund McMillen himself has stated several times that the resemblance is purely coincidental, because he has never watched (nor even heard of, prior to the game's release) Fullmetal Alchemist.
Similarly, the Sad Onion is also not a reference to Stuart Ashen nor the "Not for ages 0-3" face that repeatedly appears on the packaging for products he reviews.
The Necronomicon's cover (which looks like a distorted or disfigured face) is the same as in Evil Dead.
The Wire Hanger item is a reference to the film Mommie Dearest, in which an abusive mother screeches the famous quote: "No more wire hangers ever!"
One of the new items in Binding of Isaac: Rebirth, is the Ludovico Technique, which leaves Isaac's eyelids pulled back, as in the classic scene of Alex's reprogramming.
The Dople (a skinless Isaac's doppelganger in The Womb) is a reference to Tomb Raider, where a skinless enemy who mirrored Lara's movements had to be killed by being lured into a lava trap, similar to how Doples can be lured into spikes.
Two new pill effects in Rebirth are "Lemon Party" (a reference to an infamous Shock Site) and "R U A WIZARD". (Lemon Party drops a very large, very damaging Lemon Mishap puddle, while R U A WIZARD gives Isaac temporary Fish Eyes that force him to fire each shot at a 45 degree angle instead of straight ahead.)
Actively defied in one particular case. Many people were expecting references to Northernlion, Bisnap, or other big names in the TBoI fandom, but Edmund has stated that he intentionally avoided such references in case he accidentally left someone out.
Although, there's a little nod to a certain meme started/nourished by Northernlion. "Rebirth Got Canceled" is one of the new Fortune Teller message, which was a popular joke statement back before the game's release,note and it's still used around some parts, despite it being out! and a thinly-veiled Take That towards Phil Fish, who decided to cancel Fez 2 after a particularly bad meltdown.
Crack The Sky is a reference to King Lear, but also to an album of the same name by Mastodon.
Two new pills added in Afterbirth are "One Makes You Larger" and "One Makes You Small", referencing the Jefferson Airplane song "White Rabbit". Presumably they'll still work if you get them from Mom's Coin Purse/Mom's Bottle of Pills, though.
Afterbirth added an item called Black Powder which lets you draw circles of (what else?) black powder to form pentagrams that deal damage to enemies standing in the area. Its in-game hint text? Spin the black circle.
There are 3 very hard to unlock items called The Body, The Mind and The Soul. Their descriptions are respectively "I feel all", "I know all", and "I am all". They are a reference to the movie Highlander, as the three are said almost verbatim when MacLeod wins The Prize.
One possible reference might be the Dead Boy achievement, earned by not taking damage in the Chest room or its Dark Room variant. The Chest is famous for having the great big golden door that leads to the Lamb. Life has many doors,Dead Boy!
The pickup quote "Game breaking bug, right away!" is a reference to a quote by Phil Fish in Indie Game: The Movie, where he says the exact same words when a bug is discovered in FEZ on the first day it is being shown at PAX. This has been confirmed by Edmund himself on twitter.