I want to bake a material to an image for use in an external program without shadows but if I don't use a lamp the result is too dark. Is there a way to add light to the material without adding shadows, or is there another way of getting the material onto an image for export?
Blender provides settings for this. Use Diffuse (on) Direct (on) Indirect (on) with the rest (including shadow) turned off. This will bake only the light that directly comes from the lamp.
Alternately, you can use the "Diffuse Color" pass to get JUST the color, with no lighting at all.
A note about bake time: Baking will use your render settings, so if you have set up to render a lot of samples, baking will take a long time. Time to render is quite linear, though, so if you bake 5 samples and divide the time it takes by 5, that will be how long each sample will take, and you can use that to estimate pretty accurately how long a bake will take. You could just to 1 or 2 samples to benchmark, but there's a little bit of imprecision in how long any given sample takes. Calculating from multiple samples evens that out.
From the Manual:
Combined Bakes all materials, textures, and lighting except specularity.
Combined Pass Options The passes that contribute to the combined pass can be toggled individually to form the final map.
Ambient Occlusion Bakes ambient occlusion as specified in the World panels. Ignores all lights in the scene.
Shadow Bakes shadows and lighting.