What makes you think "yeah that's league of legends" when you think about it or reminds you of the game when you think about it.
For me it's the Arcade theme and Garen. My first days of the game were spent playing Garen and the Arcade theme is just great music that I listened to for a long time. It is cemented into my mind as "league of legends" music now.
Katarina and Ryze are the posterboy Champions for League for me.
The announcer is pretty iconic.
How the currencies are all "points": IP, XP, RP, CP, LP
EDIT: Poros 
Getting flash ulted by 
I love League of Legends
Probably aram, used to play it with buddies in college in customs long before riot made it permanent. Still made plays for dragon & baron, but otherwise tried to share the middle lane.
Seeing a champion that gets me excited to play another round. For example, seeing Kayn made me incredibly excited. I can't wait to get him and learn how to play him, because his dual nature is so exciting to me. I know most people aren't hyped for Kayn, but while I am excited for Urgot I much prefer Kayn, due to how hilariously edgy he is and how cool he seems.
Old SR Music, Various Old Champion Portraits, Pebbles and Rats in scout uniforms.
Arcade login theme is called "Bit Rush" and it's available on iTunes
The random downvoting of people's posts.
"Welcome to summoners rift"
Toplane
after all it is all there is to this game right?
