I have to admit, I'm somewhat biased on this; I've always done extensive prewriting (or, at the very least, preplanning), and I've never really just winged it for a story. I say that you should always do a bit prewriting, even if it's just a page or so; and I'm sure that everyone has heard this before, but it does help you flesh out your world, plot, and characters that much more.
Let's start with my favourite method: Free Writing
This can be done several different ways, but I've always free-written, when writing Fiction, by selecting a few characters and writing a few pages with them. It can be centered around a conversation that I want to include, but I don't know where, or a cool scene that I'm not going to get to for a while, but the point's that I just get some writing done that may be important to the story. I've actually created one of my main characters (who was originally just a throw-away extra) and several of my major plot points during free writing.
If you're a more artistically minded, but still like to see how things connect type of person, then Webbing/Clustering might be bit more down your alley. To begin a cluster/web chose a plot point (maybe the conflict or main character?) and keep writing down (and connecting) other plot points and relationships with other characters.
Personally, this has never really helped me; I lay more on the logically-minded side of the spectrum. What helps me, when I'm not free-writing, is listing and story specific questioning. Listing is simple, though I recommend that you have an ending in mind before you begin; what you do is write down the beginning and the ending, leaving plenty of room between the two. Then write down all the events that connect the first and last events.
Story specific questioning is where you answer questions related to your story in order to flesh out your characters.
Character Questions In depth
9 Character Questions