The game contains references to a recurring joke involving "Darkness" contacting various characters, which dates back to Warcraft 3's Dread Lord and Demon Hunter units.

If you click on Valla enough, she will make a reference to Elmur Fudd from Looney Tunes with the line "Be vewy vewy quiet. I'm hunting demons!"

Sonya references the 1982 Conan the Barbarian movie's "What is best in life" speech and the amazonian women from Futurama when you click on her.
She lists off Conan's "best in life" ambitions, skipping the line about hearing the lamentation of the enemy's women.

She also says "You, death by snu snu,", which references the Amazonian execution sentence in Futurama.

Malfurion's 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.

Tychus's 2nd palette for his base skin replaces the pin-up girl on his armor with Widowmaker from Overwatch.
His 3rd palette replaces the pin-up girl with Tracer, also from Overwatch.

Queen Nightshade's line "what a joyous night to have a curse" is a reference to Castlevania II: Simon's Quest, and the text box reading "what a horrible night to have a curse", which appears during the transition from day to night.

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.

He also recites The Konami Code.

The game was originally called Blizzard DOTA, and was planned as a custom game for Starcraft II, but the name was later changed to Blizzard All-Stars after trademark disputes with Valve. Some time after, the final project was renamed to Heroes of the Storm.

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.

Rotating a hero in the character select screen too fast will cause them to go into a stun or dizzy animation state.

Kharazim's default skin's third tint 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).