Let's see I saw references to Sonic, Mario, Q*Bert, Pac Man, Donkey Kong, GTA, Katamari, Bomberman, Metal Gear Solid, Duck Hunt, Angry Birds, Bubble Bobble, Excitebike, Mortal Kombat, Street Fighter, Minecraft (I think), I'm guessing Scott Pilgrim, and there were several I knew were game references I just couldn't recognize the games they were referencing.
Edit: As for individual references, I counted roughly 31.
I saw this a bit earlier on YouTube, but this time i actually tired to spot the different references. And most of them went totally by my head...
But I was surprised i didn't saw Keyboard Cat the first time.
0:34 Is Parodius
0:39 is Elevator Action
0:43 is Pitfall, Mortal Kombat(or Marvel vs Capcom), and either Kung Fu Master or Another World (stomping scorpions with a foot sweep)
0;47 The backgrounds is from Two Crude Dudes, I believe.
1:04 is Splatterhouse/Killer Instinct
1:13 The Girl Boss throwing up is probably based on Vice or Mature from KOF, who has that as one of her winning poses.
(mostly got by people earlier)
3:00 Effing Hail
3:02 I know that flag is relevant but...
3:19 (and most of that sequence is Primal Rage/Rampage)
Thank you, Rise of the Triad. For those ludicrous gibs. They're truly the best. Also a big fan of the Fist of the North Star (or possibly God hand) with the Mario Star. Combining references makes it even nerdier!
Also, fairly certain the final scene is meant to reference Neverhood, as the face styles seem a lot like their brand of claymation. Then again, I don't currently own Clayfighters so I dunno. I will say they mostly focused on console games, but at the same time, they had a pretty big range of references, soooo, it's anyone's guess.
Edit: Is that Gish hiding in the Q*Bert stage? (0:44)
More Edit: While I'm at it, 1:08 MIGHT be a Disgaea reference, as I can't think of any other games that use team ups in that way. I'm sure there is, but I'm not familiar with it.
Revenge of the Edit: Well, apparently, if you look closely at the glass wall at 1:04, you can see the main character from Dig Dug, pumping up, as it were.