Here's an example of a shot I took indoors with no flash. It was during the set-up process of a Christmas dinner/play that my school does (which I take part in). Because we were still setting up, the windows weren't yet covered, which was letting in a lot of blue light from outside. I wanted this shot to be more cozy and feel like the holidays, however, so I used the "Cloudy" preset. This preset adds warmth to your colors, as cloudy light tends to be blue and cool.
click to enlarge, or see it on Flickr
I like how it turned out—warmer than the light in there really was, but it captured the feeling I was after.
Try fiddling around with your white balance from time to time. A lot of cameras these days have a manual setting (mine included) which can make for some very interesting colors if you "set" it with some other color besides white. Post links in the comments!