Here is some of what he said:
"To all the people watching, I can never thank you enough for your kindness to me, and I'll think about it for the rest of my life. All I ask of you is one thing: Please do not be cynical. I hate cynicism – it's my least favorite quality, and it doesn't lead anywhere. Nobody in life gets exactly what they thought they were going to get. But if you work really hard and you're kind, amazing things will happen."
-Conan O'Brien
Cynicism is one of those words that gets thrown around a lot, and is often used inappropriately. Cynicism is born out of frustration with a person or a situation. Cynicism is not the frustration or the disappointment itself, but it is where these feelings can lead to.
It is a distrust of someone's motives.
Cynicism is the thinking that some organization or person (usually in authority) is "out to get you" in some way. It isn't cynical to be critical of something to foster improvement. It isn't cynical to be frustrated with a situation. It is cynical however to take this frustration or disillusionment and start constructing a scenario where you are being deliberately persecuted or plotted against.
I see cynicism the most in two places...also the two things you probably should never bring up at some sort of family gathering: Religion & Politics.
No need to list out specifics...I'm sure you can think of plenty of instances in both arenas where people are cynical. Or where you are cynical.
Either way, I believe that what Coco said was right. That cynicism never leads anywhere. I believe that it's completely unproductive. And more than that, when you find yourself being cynical and promote that mindset internally, it can begin to really destroy who you are.
*Ninja Edit*
Here is a clip of his end of show monologue in case you were interested.