I would say I work semi-organically when it comes to color. I am most often inspired through my research phase and immediately start designing with color and work with variations as I design. I've actually never used any of color palette web sites that some are posting, but I will definitely add those to my mix as a resource. While researching, my color palettes can spring from inspiration from many different things, like walking around taking pictures, reading or surfing pinterest.
Once I have an idea in mind, I make sure that the design fits the tone and audience or like others, I source from an image I am using. Because color influences people, I am careful to choose colors that elicit certain emotions, much like the yellow I chose for project one to cause a sense of anxiety, like what Mary Beth was posting about. I'm definitely sensitive to the mood a color gives us and even think about this a lot when I am decorating at home. Color theory is really interesting and I think it is very important in design, but color is also largely tied to our own very personal experiences so it can always be tricky/theory doesn't always hold true.
For me, it all depends on what I am trying to communicate with the project and what color helps deliver that message. It's a lot of trial and error sometimes - but asking others who aren't invested in the project how something makes them feel is always a great help.