In the beginning of Episode One, Dog suggests getting Alyx and Gordon into the Citadel by tossing a car (with them in it) across a gap into the building.
Alyx: Well, Gordon, unless you have a better suggestion...he is a robot, he's done the math.
*Turns to Dog*
Alyx: You did do the math, right?
Dog: *Shakes head no*
In addition, if you listen to the developer commentary, you'll find out that this joke started because of a glitch in which Dog's head shook back and forth after Alyx mentioned him doing the math. The play testers loved it so much that Valve made it official.
Also in Episode One, Kleiner is making a televised announcement and mentions the benefits of removing the reproduction suppression field the Combine had in place.
"Did Dr. Kleiner just tell everyone to get busy?" "Yes Ms. Vance. Yes he did;"
You can derive great fun from throwing things at the officers in Half-Life 2.
In Episode 2, where you have to help Greggs and Sheckley fight off the Antlions, after Alyx is revived by the Vortigunts and Alyx and Gordon are on their way riding up the lift, Greggs yells "Alright Gordon, be adequate!", to which Sheckley asks him what the hell that means. Greggs simply replies, "I don't know, sounds like something the Vortigunts would say."'
Earlier, they comment that the Antlions shouldn't be bothering much unless someone has been messing with the grubs—this after the player had most likely killed dozen and dozens of them for health or the the achievement.
Let's see: You've got standard objects like exploding and non-exploding barrels, but there are also things like tires and boxes. And if you're just feeling silly, you can toss paint cans at them!
When you enter the Victory Mine, you see these little immobile grubs all over. Because you can easily kill for health and there's even an achievement for getting all them, you'll probably try and kill as many as possible. When you reach Griggs and Sheckly's outpost they say the Antlions don't make themselves too much of a problem so long as you don't mess with their grubs. Whoops.
In Episode 1, there is a moment where you have to crawl up the air ducts and temporarily leave Alyx behind; however, if you go too far down the wrong path you fall through, in the same room where you started from right in front of Alyx.
