The brown color of feces comes from the pigment stercobilin, one of the final products of heme (red blood cell) breakdown. Urobilin is similar; it also comes from heme catabolism. However it is yellow and excreted in the urine due to high water solubility. Changes in fecal color can indicate a wide range of issues, in the appropriate clinical context.
It does change, but you might not notice it depending on how much you change things. Go eat a lot of orange sweet potatoes or carrots (orangish-brown) or dark green veggies (greenish-brown) or beets (a very unnerving blood-like color) go very low fat for a few days and then eat high fat (light grey-light yellow).
There's also the reaction of bile and destroyed red blood cells that /u/barloo_the_bear discussed.
Is there any nutritional value left in our feces? I imagine this would largely vary depending on diet?