It depends on the game. If I know the MC has a particular set personality/backstory, I won't. Otherwise, I'll do varying degrees, maybe I'll fully self-insert (Especially if conditions are just right, with a LI I really like and dialogue options that suit me perfectly), maybe I'll develop an OC/sona-esque character that kind of meshes the story and myself.
I notice that for shorter games I tend to self-insert more.