I was hoping that y'all could talk about how your ideas originate. Is it just random inspiration? Is it from other games? Real life?
Sometimes I think about games I like or haved liked in the past, and want to make something similar. These are often very big games, so I focus down on one aspect instead and make that.
More frequently I think about game theory, interactivity, and probability models, and make a game to form an experiment. In particular, procedural generation models dependent on player interaction are the most fascinating. These are often my games that get finished, but they are generally raw and non-interesting enough(and nongraphical) that I have no intention of showing them. I've found that ludological approaches can invite a shitstorm of debate around these parts, so I'll say no more on that.
I have a huge file full of game ideas I have yet to play with, these are often more intimidating, "big" games that would actually be fun to play. Some of them do focus on gimmicks in established genres, like games you mention, and that's more a case of, "Here's an interesting gimmick, how can I fit it into a gam?"