My game AirScape was planned quite... interestingly... I wouldn't exactly advise this method...
I wanted to do a platformer, then I thought it would be cool to have it gravity shifting.
Then I decided simple foresty theme would be the most effective for my meager art skills.
I decided robot enemies for the same reason.
I couldn't come up with a character for ages. I chose a dumbo octopus after ages of really random possibilities.