There are four standard emotes that you can use in League of Legends. You can joke, you can taunt, you can dance, and you can laugh.
Obviously you can use these for fun, or you can use them to pester your opponents as well.
Joke Emote – Type /joke in chat and hit Enter, or bound by default to Ctrl+1
Taunt Emote – Type /taunt in chat and hit Enter, or bound by default to Ctrl+2
Dance Emote – Type /dance in chat and hit Enter, or bound by default to Ctrl+3
Laugh Emote – Type /laugh in chat and hit Enter, or bound by default to Ctrl+4
All of these can be changed in the key binding section of the menu. Check out my other guide if you need help configuring your key bindings.