How much planning before coding?

When you guys start to write a new (a game that you made up) game, how much planning do you do before you start the actual coding? How much planning do you have to do for a game that already exists, but you are remaking it as a computer game (like chess, etc.)? Do these two time amounts differ?

Before going into of my own creation I would advice to at least
-Complete much of the gameplay aspect design
-Brainstorm any major complications and work out how they can be resolved on paper
-Get a general idea of the workings of the finished code
For a game like chess the main thing is to get the AI working. For that I would probably make pseudo code or grab some from the internet.

EDIT
Personally, I think how much time you spend is more just a matter of personal preference. Some people might be able to design on the fly while others may need to spend days desigining.

EDIT 2
For me, those times would differ. Mainly because I could grab some already made ideas for a game like chess off the internet while for my own creations I can't do that.

How much time do I spend brainstorming about the game?

Lots.

I get an idea for a game.
I open up MSVC 6.0 and start a new project using NeHe's openGL template
I start adding media management functions - load textures, models, fonts
I add the common utility functions - timing, input structures, etc.
by this time, im bored and tired of coding.
I start thinking about the game hierarchy, the abstract interface of objects and events. I also start considering level management and how the world will work.
I start coding the basic game object, and linked list functionality. I start deriving management classes for levels, menus, etc.

At this point I go to a strict code while brainstorming process. I just start working at the smallest part of the game design and working my way backwards to the management classes, revising as I go along.

as a member of the industry, I'll tell you what my thoughts are (not to say you previous posters aren't professional game designers/coders). You are pretty much required to have a complete design document and technical document written before beginning a project. The design document has all of the gameplay, story, and user experience issues layed out in black and white print. Of course, balancing issues will be fixed after the product is near finish, but you need something to build off of. If you ever have phrases like "might be able to" or "should probably," then more thought needs to be put into the document.

The technical document lays out how the code modules will work together. It won't be complete code, and some may not even have pseudo code. However, you should have a plan of action, and a concrete idea as to what each module will do.

These are not the only aspects that go into the pre-production phases, but the rest is more along the lines of coding standards and backup plans. As far as the actual design goes, that is what you should have.

The purpose of all of this is to help the project and all the people working on it. If it isn't necessary to keep everyone on the same page, then there won't be a whole lot of work put into it. So if you're taking the loan wolf approach, chances are you won't need to go so indepth into your design. Although, it's not a bad idea to document it, that way you can look back and see where your thought process was wrong.