Dance: Befitting the Korean origins of her inspiration, her dance is Run Devil Run by Korean pop group Girls' Generation. A side by side here.
To complement this, Ahri is gaining a 'Popstar' skin, which is another nod to this particular reference. On top of this, the announcement of this skin coincided with the release date of a Girl's Generation album, and the skin comes with another unique dance referencing them.
Skins: Sherwood Ashe gets her name and primary colors from Robin Hood. Woad Ashe looks like Guinevere in the 2004 film of King Arthur.
Skins: iBlitzcrank's design is much like the Apple Macintosh, and was released alongside LoL's beta client for Macs. The name itself is a reference to Apple's line of electronics which have a similar naming scheme (e.g. iPhone, iTouch).
Ironically enough, when iBlitzcrank dies he suffers a Red Ring of Death; a reference to the Xbox made by Microsoft, Apple's main competition.
Skins: Apocalyptic Brand looks like he just stumbled out of the Fallout world.
Brand's origin seems to have been born out of Surtr, with Brand's body being an essential viking, his appearance being similar a common description of Surtr (blackened skin with lava crackling in it), and his claims that him burning the world will renew it, as would follow Surtr's role in Ragnarok. Regretably, Brand has no Flaming Sword.
Skins: The splash art for Jurassic Cho'Gath, with Cho'Gath in a museum-style building with a large banner hanging overhead, is a reference to the Jurassic Park film.
Quotes: One of his lines "Today is a good day to die!" could be one to Star Trek, but possibly instead to Sitting Bull or Crazy Horse. He says a line from The Charge of the Light Brigade verbatim: "Ours is to do and to die." He also says "For my father, the king.", a line of Prince Arthas from Warcraft 3. As one of the developers worked on Defense of the Ancients: All-Stars, a Warcraft 3 custom map, this was quite certainly intentional.
A somewhat elaborate example; Karthus' innate passive's icon, Death Defied was originally a picture of a sheep crossed out. One of the most powerful items in DotA is Guinsoo's Scythe of Vyze, which turns people into sheep. Guinsoo uses Karthus' icon in the official forums. You make the connection.
Skins: His Harbinger skin is somewhat reminiscent of Emplate.
Lux is largely based on Marisa Kirisame from Touhou. Her ultimate is named after Marisa's Final Spark (a variation on her trademark spell known as Master Spark), which is also a giant rainbow laser beam. Lux also calls herself an "ordinary witch," while Marisa is The Ordinary Magician, and both are known for copying spells from other people. Finally, Lux's Sorceress and Spell Thief skin may be based off of Marisa, most notably the witch's hat and broom on sorceress and the similarity of the outfit and wand of Spell Thief to Marisa's outfit in UFO.
Skins: Her Commando skin is based on the Imperial Guard from Warhammer 40,000. Bonus points for having a wand that's pretty much a lasgun on each end.
Skins: His Chosen skin is pretty much a Jedi knight, complete with blue, green, or red light saber depending on how much his attack damage is increased by his Wuju Style ability. His Headhunter skin is based on Predator.
Skins: He's basically a walking homage to Predator. His Headhunter skin makes this more apparent.
Dance: His dance is the Haka, of rugby's All Blacks fame. This may further be a reference to the similar looking Charr race in Guild Wars, as they also use the Haka as their dance animation in Guild Wars 2. Very possible as the Lead Champion Designer Morello worked on Guild Wars 2, and Rengar's release very closely coincided with Guild Wars 2's.
Skins: Her Redeemed skin is based off of Meliadoul.
Skins: Her Warrior Princess skin is Xena, her Spectacular skin is Wonder Woman, her PAX skin is based on TRON, and her Huntress skin resembles Zhu Rong, which turns her weapon into a boomerang (her preferred weapon until 6).
Skins: Arcade Sona's ultimate (which sends out a wave causing enemies to dance) resembles a Dance Dance Revolution screen, with a flow of arrows pointing in different directions.
It's generally accepted that her standard skin was inspired by Hatsune Miku.
Skins: His form while using his ultimate is awfully reminiscent of a Lord of Change. His Tyrant skin makes this even more obvious.
Abilities: One of them is called Nevermove, a pun on Nevermore that was only supposed to be used during development but ended up sticking.
Abilities: One of his skills, Tides of Blood, may be a reference to an old MOBA-styleWar Craft 3 custom map of the same name. Said map had a "Blood Mage" hero who had more-or-less the same gimmick as Vladimir.
Skins: Shurima Desert Zilean looks a bit like Gwonam.
If two or more champions perform their dance emotes in front of Vilemaw, the giant spider boss of Twisted Treeline, he'll lift his legs up as if surprised, look around to make sure no one's watching, and start doing the Carlton Dance.
The two new shopkeepers on the Howling Abyss map will occasionally reference movie quotes:
The icon for Mastermind in the support mastery tree is a reference to the box art from Deus Ex.
Youmuu's Ghostblade is one letter off from Youmu from Touhou, who also wields a ghostly sword. It is a katana with sakura petals flying around it.
Wriggle's Lantern shares a name with a firefly in Touhou. The official statement is that it was named after an adjucator called Wriggle, but behind the scenes we know that (former) employee Shurelia is a big Touhou fan.
Trinity Force is the most expensive item in the game, created by combining three different mid-level items into one hybridized one. Both its name and its in-game icon are a shout-out to the Triforce from the Zelda series.
The Brutalizer item costs exactly 1337 gold in total.
Rylai's Crystal Scepter is named after the lore name of Crystal Maiden from Defense of the Ancients: All-Stars. The item icon is almost identical to the one for Rylai's Brilliance Aura ability.
The Manamune is highly reminiscent of the Soul Calibur sword from the first few games.
Its name is also derived from Masamune, a legendary Japanese swordsmith. Its upgraded form, Muramana, is the same case; Muramasa was also a famous Japanese swordsmith.
Atma's Impaler references the "Atma Weapon" mistranslation of Final Fantasy VI. Just like the weapon from the Final Fantasy game, the strength of Atma's Impaler is based on the wielder's HP.
Guinsoo's Rageblade is half shout out and half internal homage, as Steve "Guinsoo" Feak, one of the big names at Riot Games, used to develop Dot A Allstars before passing it on to current developer Icefrog. For that matter, a number of champions and items take their moniker from Riot developers' screen names. But the most convoluted Easter Egg is the fact that Karthus's passive used to have a sheep as an icon. This referred to "Guinsoo's Scythe of Vyse," an item from Dota which conferred Baleful Polymorphing, and was snuck in because Karthus is Feak's favorite Champion.
An update for a more exact queue status now shows your place more precisely. Initially, when the queue was long enough, it just reports your current place in the waiting line as Over 9000. The queue is now more exact (Over 20,000), but lost the reference.
The in-game chat displays kill streaks using Unreal Tournament lines, such as "Killing Spree!" "Dominating!" and "Godlike!"
One example from the Journal of Justice that coincides with Getting Crap Past the Radar is Janna being caught in the middle of a scandal that's heavily implied to involve a sex tape, and trying to pass it off as boosting her magical reserves, bringing to mind the notorious "Mana transfer" in Fate/stay night.