FPS - The person who keeps the respawn screen warm. :P
MOBA - Wherever really, I'm usually one of the last to lock-in and tend to go with whatever needs filling as I can generally do any role.
MMOs - Again anything really, my mains tend to be healers but I usually also have a tank and dps characters too.

RPGs - I explore as soon as the game lets me. For example I managed to clock around 120 hours of playtime on Skyrim before I ever went to top of the mountain to visit the Greybeards (I think that's who there are) which is like one of the first quests the game gives you