I’ve always started my projects from the player character gameplay mechanics first, then AI, then environment. After doing the Stealth tutorial, I found it enlightening to start from the opposite side, environment first then, player gameplay. This got me wondering where is the best place to start when designing a game?
Whatever works for you? Maybe there isn’t a best way other than the one that helps you to express yourself fully and in a natural manner.
I usually start with the central core essence of the player and control system but that’s just me… but then when it comes to implementing the design it usually starts with environmental stuff because you sort of need that in order to put the character in the environment.
I vote gameplay. Because if you start with environment then you are sort of trapping your gameplay to that. But I guess it would depend what’s the “hook” of the game. But whatever keeps you motivated to finish the game is good. Sometimes you need to do some eye candy to keep the project exciting enough.
eye candy is true. I made some Ghost Recon: Future Solider/MGS4 mechanics not to long ago, and it played really well, but my characters and environment were bland, so I lost interest. When I did it the opposite and my environment was fully realized, I kept going a little bit longer.
Well, with design, I start with a story. For that, I always begin with the enemy, since all great stories (I think) should revolve around a great bad guy. The hero typically does little more than react to the enemy, which then makes them heroic.
As far as building the game; I know this is stupid and backwards, but I build that game in the order that it will be played. So I create my main menu first, then have it load up the character, stats, first level, etc.
That “first level” is usually just a throw-away level that I create which holds everything that can possibly be done in the game. I build all the features in that level, then I start creating the world.
As far as pipeline goes, I write up some notes. Then I code some core mechanics. Then I put together a detailed design doc (and a pile of index cards, detailing all of the classes in the code). Once I have something working, I start harassing my artists to make it pretty.
Well, I heavily begin with a design doc. I want to know exactly what this game is and will be, what it will look like in the end. Then, I do terrain, then programming, then characters and assets 
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I do the combat first but… I use rigid body weapons which means I need a full suite of animations - which is usually accompanied by fairly polished models and textures. Then I build a level as a implement other mechanics… I just keep going after that and add mechanics/puzzles as I need them…
Well, game design should start with a game design document. Flesh out the basics, then prototype.
It all depends on the game type, prototyping for an FPS game is vastly different to prototyping a point and click adventure.