I've had great experiences with Kuler and now Adobe Color CC. It keeps changing on me with upgrades of Adobe products, but I have had my Kuler account linked inside my InDesign and been able to access color palettes I've liked or created. I've also been able to see and access all kinds of codes there, including CMYK.
I find it helpful to search on themes and pick and choose colors and recombine the ones I like. I have used Design Seeds in this way, to get ideas and then change pieces around. I've also turned to Pantone for upcoming color trends.
I usually have colors in mind as I start a project and then change them as I work and think about the subject matter and the target audience and what the project is saying. As Jen and Rachel mentioned, artwork is a good place to start. Feedback from co-workers, classmates, and a spouse is very helpful. I'm working on a promotional piece for my association's convention in August, and the colors have changed based on the gadgets we've chosen to give away -- the colors we can get them in.
Looking at everything around me is helpful and inspiring -- the newspaper, magazines, TV shows and ads, ads on buses and in the subway, art, buildings, gardens, etc.
