Do your Characters dictate your story?

Sometimes people ask me where I come up with things.  Its simple...the characters lead the way. 

There's a Luke Wilson Movie, Alex and Emma that I think describes writing for me perfectly.  First off Wilson's character feels the pressure and brings up a brain tumor.  That makes my husband and I laugh.  Not that the Tumor is funny by any means, but because several years ago, an irritating sound in my right ear had the Dr. sending me for an MRI to rule out a Brain Tumor, so the irony of that scene was not lost on us.  After that he goes on to explain to Kate Hudson's character that the characters in his novel tell him where the story will go.  They tell him the story.  And that is very true for myself as well.  When I sit down to right, I have a vague idea of my plot and I develop the lead character, and then the rest just appears on my computer screen as I go. 

Take my writing prompt, for example, that I wrote last week.  I was given the mission....the story requirements.  I developed a character by what she says in the first sentence that I used from Alice, but after that it was out of my hands.  Yes I made some of the decisions.  I decided that the business would be an advertising company.  And yes I decided to leave my characters very one dimensional and predictable , but the turn of events, right down to the "What would you like with your fries" ending, was nothing I planned for.  I had no outline or destination for this story.  I just started writing and that is where it ended up.  Not my finest work, I know, but I wrote it in between errands for my husband's grandmother's funeral...so all things considered, not horrible.

My Novel is the same thing.  I started with an awful title and a character.  One day weeks later I came up with a funny, catchy, little title while brushing my teeth and from there it just blossomed out on it's own.  It now has a plot, a sub plot, foreshadowing, and a twist ending....none of it planned.  It just all came from my fingertips as the protagonist led the way.

So is it like that for a lot of writers or is it better to carefully plan out your work.  Is it a shorter journey to the finish line if I mapquest it first, or does it develop better maybe, because it was so open to ideas, interpretations, and detours along it's way?