The main source for humour in Shadow of the Colossus is one simple fact: Wander is very clumsy. It's one of his more endearing traits.
On top of the cliff over looking Barba's lair, you can grab onto a large hawk and go for a ride. If your grip gauge is big enough, you can hold on long enough to have the hawk swoop around and slam Wander into the cliff.
The area also has a bunch of tortoises crawling around on the ground. Wander can trip over them.
He tends to trip over himself when climbing up sloped objects as well.
When climbing up a wall to another platform, if you manage to get Wander parallel to the platform and close to the step, let go and he'll just kinda roll off the wall.
Sometimes when falling a short distance and pressing the sword button at the right time, Wander will get the sword stuck in the ground.
He can be made to slip out of Agro's saddle and ride squatting on her side. Why he would want to do this is unclear (it has no gameplay purpose), but he looks simultaneously awesome and completely ridiculous while doing it. As a bonus, the animation for him getting back into the saddle after this is an awkward flop.
When you defeat Malus (#16), it grabs its face, making it look like it's Facepalming.
You can have a lot of fun when you acquire the Invisible Cloak, first by riding Agro around while it seems like she's steering herself. Then a few colossi have some interesting reactions when you become invisible in the middle of battle, such as making confused sounds and searching about for you while you can stand right in front of them. Also when you engage Avion (the fifth colossus), while it's standing with its wings in the air, put the cloak on and it will fold its wings instead.
Agro is hilarious all by herself! Her model tends to lock up when she is tossed about in a fight (most notably with Dirge and Phalanx) making her legs go stiff.
She also has a habit of just running away while Wander is fighting a Colossus, adding a layer of humor to the whole event. Agro just projects a sheer "Screw This, I'm Out of Here!" vibe when this occurs.
Leave her alone long enough and she'll go a short distance to find some grass to eat or water to drink. She will also even eat dirt or sand, if that's all she can find.
The lizards found all over the Forbidden Land are hilarious, if only for their silly waddling gait.
It can be quite amusing swimming around Pelagia (#12) to get to its back as it also turns to try to shoot you, making it chase its tail.
The various ways Wander can be thrown large distances include losing his grip (or letting go) as a colossus is thrashing, trick hawk-riding, and shooting an explosive arrow at his own feet. While sometimes requiring some creativity to get the maximum effect, all of these are really funny to watch.