The goat scene had me dying of laughter. So did Cassandra reading Varric's books, IB saying "I shall bring myself sexual pleasure later, while thinking about this with great respect." about killing your first dragon (didn't even have him with me at the time), the crate judgement, the Wicked Grace scene, the fearling that was named "Ironically, Spiders", Sera commenting on what sex would be like for IB and Dorian, and at least a dozen other things that have been previously mentioned on here.
I also had a pretty funny glitch in-game. I used upgraded Grappling Chain on a random archer right before he died and after I kicked him, he went flying behind me so far that I couldn't see him! 
The letters from your old merc boss if you played Qunari were pretty funny too. Especially the one after he asks for a job from the Inquisition and you have Leliana give him one. I actually want him as an actual character in DA4, if not a fun companion. 