As a marketer, I need to come up with campaign ideas that range from the mundane to out-there stunts and wacky or 'big' ideas.
For me, inspiration comes from a blend of discipline and meditation. First you lay the foundation through a disciplined process of information gathering and research to learn everything about the client/project/issue/brand until you are completely 'steeped' in it.
Then comes the inspiration part. Sometimes it's very straight-forward and the idea will emerge as you go through the research. But if this is not the case, then I need to do one of two things: I either 'goose' the process by having brainstorming sessions or I ponder/meditate on the issue while in a zen-like state, which often leads to flashes of inspiration and ideas. I can reach the zen-like state first thing in the morning, in the shower while still half-asleep, or at a certain point during an aerobic exercise session. I've gotten most of my career and reputation-making big ideas like this.
Once on a deadline for a presentation, when we couldn't think of anything, I went in desperation at 3 pm, got in the shower and prayed...