I find that my most viable ideas are ones located in my interest. I think it's more important to have a company mantra, or "stickiness," than to just find a need and fill it. This way the company doesn't just rely on one idea. For example, GM is in the transportation industry, not the internal combustion powered car industry. GM is adapting to the current climate by introducing electric powered and hybrid cars.

Big companies aren't stupid either, they expand when they see opportunity. There are individual niches that blue chip-type companies don't care about, so there may be opportunity there.

But what works best for me is thinking about my interests and then developing ideas that can better them. For a while I was trying to reinvent the wheel, but some of the most successful entrepreneurs (Michael Dell, Henry Ford, etc) didn't invent the product they sold - they just did it better.