Robot Chicken Episode 0

Reindeer: She's so ugly, we'll push her face in dough and make gorilla biscuits!

This is a reference to one of Fred Sanford's line from Sanford and Son.
For example:

Fred:(to Esther) You're so ugly, I could stick your face in some dough and make some gorilla cookies!

Composite Santa:

Composite Santa, who is one half Santa Claus and one half Frosty the Snowman, is a parody of Composite Superman: Half Superman, Half Batman.

Akira

When Mrs. Claus grows into a titanic blob near the end of the last sketch, this appears to be a take off on the animated movie, Akira, when Tetsuo grows into a massive singled-cell type of organism. When she does, the character standing, screaming "NO!" whose hair stands up on end, appears to be a reference to Tetsuo himself because of the similar appearance.

The headaches that Mrs. Claus receives is also taken from the Akira movie, as they were a precursor to Tetsuo's metamorphosis.

Dragonball Z
While it is obvious that Goku and Gohan are characters based on the popular anime, Dragonball Z, not many know that the "Spirit Bomb" they use is from the show as well.

The cloud that Gohan uses to attack the Nutcracker is based one the Nimbus cloud from the animated series.

The way Goku and Composite Santa yell is a parody of the series as well, because the animated series is known for having the slow buildups to big fights. Even the background behind Goku is remiscient of the artistic design of similar moments from the animated series.

Nutcracker
The character from "A Dragonball Z Christmas" is based on the real-life seasonal item. While the real-life counterpart is used for cracking regular nuts, the Robot Chicken character ironically knows over 100 testicle-based attacks.

The Drummer Boy:
The Drummer Boy was a homage to the movie 'Drum Line'. When the Drummer Boy marched up to Goku and Gohan (while doing a beat on his drum) he drops his sticks in a defiant way, this a a referance to the final drum line battle in 'Drum Line'.

The name of the character is derived from the Christmas carol, "Little Drummer Boy." The look of the figure's head seems to be inspired by Goku's design.