My fanfic isn't terribly complicated plot-wise, so I mostly plan things out in my head (the best place to think is in the shower). For my original stories, I like to have at least a basic outline, and I have fairly lengthy profiles for all my characters. I also have lots written about the worlds themselves, almost like an RPG sourcebook. It's all malleable, but it's very nice to have something to fall back on when I wonder "how does [character X] react to this?"
The more you write for a character, especially an original character, the more familiar you will become with him/her. After a time, you don't need notes any more, because the character has taken on a life of his/her own inside your mind. I've written entire conversations between some of my OCs without any prior planning. I just start with a situation and they talk amongst themselves, so to speak.
If you're writing a story with a long and complex plot, outlining is pretty much a necessity. You need to know what's going to happen and in what order, and writing it down is infinitely easier than trying to juggle it all in your head. That way you can refer to your outline for the basic happenings of a scene when you sit down to write. Then it's like a director shooting a scene; he already knows what's supposed to happen, so now he just has to figure out how it's going to happen.
For something complex, like a fight scene, you might want to block out the entire fight in detail before you sit down to write. Once you've got the mechanics of the fight (who does what to whom and when) established, you can concentrate on making it sound cool.
These are just generalities. Every author has a different system and writing process. Just go with whatever results in the best material.