http://heroesofthestorm.gamepedia.com/Kharazim#Trivia
The third tint of Kharazim's default skin references Aang from Avatar: The Last Airbender, a monk with a blue, arrow-shaped tattoo on his head.
The second tint of Kharazim's Jade Dragon skin references Aang's predecessor, Roku. He wore red and black clothing with a fire motif, and had a white beard and topknot.
The third tint of Kharazim's Jade Dragon skin references Goku from Dragon Ball, a martial artist known for wearing orange and blue (and, as a Super Saiyan, having bright yellow hair).
http://heroesofthestorm.gamepedia.com/E.T.C.#Trivia
When you click on The Elite Tauren Chieftain in the selection screen he says "I bring the Megadeth". This is a reference to the Thrash Metal band, Megadeth.
0:15
2:44
One of Gazlowe's quotes "You ever dance with the devil in the pale moon's light" is a quote from The Joker in the 1989 Batman movie.
Also in the Gazlowe video at 1:29, you can hear the Konami code.
http://heroesofthestorm.gamepedia.com/Malfurion#Trivia
Malfurion's gag quote "I am an archdruid, not a prophet. Get your lore straight." is a reference to Nature's Prophet from Dota 2 who used Malfurion's name and model in Warcraft DotA.
http://heroesofthestorm.gamepedia.com/Sonya#Trivia
Sonya references the 1982 Conan the Barbarian movie.
0:36
At 0:48, she says "You, death by snu snu,".
Couldn't find a better quality video. Its a Futurama reference.
There's also these jokes about darkness calling.
0:34
0:45 - Elmur Fudd reference by Valla.
http://www.imdb.com/character/ch0029092/quotes
I couldn't find a video that actually had the proper quote in it for some forsaken reason. Ctrl+F on this page and put " It's wabbit season, and I'm hunting wabbits, so be vewy, vewy quiet! "
Zeratul
0:37
Zeratul says "speak slowly and carry a large warp blade". This is a reference to the quote "Speak softly and carry a big stick," by Theodore Roosevelt.
1:03 - There's that darkness joke again.
1:13 - Star Wars joke.
Tassadar
0:13 - joke about the huge size of warcraft shoulderpads.
0:27 - joke about how reavers aren't in Starcraft 2. and dragoons. Then how void rays are new.
0:46 - Breaks the forth wall by mentioning Starcraft 1 directly.
1:11 - He says "Here's my number. Khala me maybe,". That's a reference to Call Me Maybe by Carly Rae Jepsen.
Illidan.
0:08 - That darkness joke again.
Does anyone know where that's from? Its gotta be a reference to something.
These darkness jokes are references to the Demon Hunter and dreadlord. from Warcraft 3.
1:11 for dread lord. Demon Hunter at very beginning.