Favorite Emote and the best situation to use it in
I thought long and hard about this one because some of the best emotes are truly the ones that you come up with on your own using the /emote, as Sven has so beautifully put. So, I am going to take this question literally and tell you my favorite built-in game emote.
For those of you who know me this will come as no surprise. My favorite emote is /flirt. Some of the races flirts are just so silly you have to laugh. My favorite (pre-Cataclysm) is the Draenei Female flirt: "Are you thinking what I'm thinking?... Good. Bring ample supply of butter and Goblin Jumper Cables." Here's a list of all the flirts (Goblin and Worgen are included in case you're spoiler free).
I've found the best situation for flirting is with characters of the opposite faction when you're just trying to quest and be peaceful. Often they will /blush or /smile or even /flirt back, completely distracting them from attempting to kill you. Perhaps this power could be used for evil, and I could lull them into a false sense of security and then go Rambo on them, but that's not me.