With the release of some of the player-created hats, it really just begs for this. Brainslugs, for instance. The same update also gave us a nice Elvis Presley reference with gelled-up hair and sunglasses for the heavy, named "Hound Dog".
A handful of the voice clips that play when dominating a player reference the infamous milkshake scene from There Will Be Blood.
The Carouser's Capotain was initially submitted under the name The Inquisitor, and while the name was sadly changed before final release, it still has the truly befitting description of "Suffer not a sentry to live".
The Spy and Medic can get a cool bowtie to wear. Its name is "Dr. Whoa". If you need more proof of what it's referencing, it was released on the show's 48th Anniversary. (For added fun, wear the Familiar Fez with it as Spy.)
A secret page in the Pyromania Update gives us a rather subtle one to a Robot Chicken sketch.
"TF Industries agreed to shoot a monkey into space for one dollar.
The Half-Zatoichi is a reference to a film series about a blind swordsman. The half part refers to the fact that the characters who wield it are half-blind in some way (Demoman has one eye while Soldier has his vision obscured).
The Holy Mackerel's item level is always 42 for all players.
One of the Scout's domination taunts mocking the Engineer:
The Heavy often says his fists are made of steel. This is almost certainly a reference to when Rocky was fighting the huge Russian Ivan Drago, where Drago says Rocky's fists are made of steel. (And now he has a melee item that literally gives him fists of steel.)
When the Heavy taunts with the KGB, GRU, Warrior's Spirit, Fists of Steel, or Eviction Notice equipped, he will perform several uppercuts in succession like Mr. Sandman in the NES version of Punch Out.
The Heavy sometimes says "I Live!" and "Run, Cowards!", just like Sinistar.
The third Halloween update introduced a mutant fly costume set for the Engineer. Fittingly enough, the set is called The Brundle Bundle.
Amid other shoutouts already present, the Engineer's Gunslinger is quite similar to the Miniturret Glove from the Ratchet & Clank games. Given how off-the-wall TF2 is, it is right at home. Granted, the Miniturret Glove didn't require Ratchet saw his arm off. The Engineer's Wrangler appears as an Atari 2600 joystick (more or less) and after a minute or so of continuous fire your character will work out the cramps in his hand as soon as fire is released which can only truly be appreciated by someone who played a 2600 game long enough to get a hand cramp.
The Medic has goggles in one of the community updates. Their name? Ze Goggles. To further the joke, their item description is "Nothing", and that was before new descriptions for other items poured in. (Ze Goggles, incidentally, are straight out of Ghostbusters.)
The Medic's Vita-Saw looks like the syringes the Little Sisters carry.
So much so that even though it was a community weapon, Valve went ahead and got 2K's permission before adding it.
The Sniper has a bobblehead of the TFC "Hunted" (i.e. Civilian) model in his camper van.
The Sniper's parents are an Australian Eustace and Muriel! Confirmed by the artist herself. (It was a running gag in the fandom that his parents were Eustace and Muriel.)
The Pyromania Update gives the Sniper a set called "The Urban Professional", which includes a black knitted woollen hat and round dark sunglasses, just like Leon (or, The Professional), who was also quite a sniper.
The comic "Blood in the Water" reveals that New Zealand in the TF2 universe is basically Krypton, with the Sniper (who is revealed to born there) being launched to Australia in a rocket and discovered by the Mundy family a la Superman.
The Spy achievements feature references to several influential spy shows and movies:
The Saharan Spy kit includes a knife called "Your Eternal Reward" (Additionally, its function, killing the target, causing their body to vanish, and disguising the Spy as them, is markedly similar to the Stealth Consume from Prototype.), a revolver called "L'etranger", and a hat called the "Familiar Fez", a reference to a quote to Austin Powers: The Spy Who Shagged Me, where Austin told a fezed mook from the first movie that he doesn't remember his name, "but [his] fez looks familiar.
There's also a Billy Joel song called "The Stranger" about putting on the faces of other people and becoming a completely different person. Might just be a really convenient coincidence, though.
The Deep Cover Operator head band is a reference to a sneaky Snake.
In the same vein, those who preordered or bought Worms Reloaded within the first week of its release received the Lumbricus Lid for Soldier, which gave him a Worms-style version of his standard helmet (complete with eyebrows), and two Holy Hand Grenades to replace his normal ones. A chorus sings out when he uses the Equalizer taunt.
The Hitman: Absolution promo has a threefer in one item: The "Deadliest Duckling" is a reference to a Running Gag / Easter Egg (that extended to even the novel and film adaptions) with an appearance by a rubber duck in every installment. The two styles are named (Al) Capone and (Charles) Luciano, and its description refers to the infamous scene from The Godfather with Jack Woltz and his horse's head.
The "Siberian Sophisticate" suit for Heavy, also from the same promotion, gives the Heavy Agent 47's famous barcode tattoo on the back of his head.
The Mecha Update page also features a poster designed as an homage to the theatrical poster for 90s-era Godzilla film, Godzilla vs. Mechagodzilla II, complete with the Sniper in a crocodile hat standing in for Baby Godzilla.
Engie's shotgun introduced in that update is called the Rescue Ranger. Does that make Engie Gadget Hackwrench?
One of the achievements, "Up All Night To Get Ducky" is a shout out to Daft Punk.
One of Scout's item sets from the Scream Fortress VI event is a Hunter costume.
One of the cosmetic items for Sniper in the Scream Fortress VI event is an ostrich-riding costume named Mr. Mundee's Wild Ride. (Alternatively, the name could reference Mr. Toad's Wild Ride from the Disney theme parks, but the Steam Workshop submission references the meme in its description.)
The Facepeeler item is a reference to the mask worn by the Joker in the New 52 comic series.
The Nightmare Hunter is based on Freddy Krueger's hat.