It's easy to customize the colors on your Basecamp account. Just click on the "Settings" tab and then click the "Color scheme" link in the light blue bar at the top of the page. There are some presets that you can choose from or you can select "Custom" and create your own palette (your company's colors perhaps?).
If you're looking for some color inspiration, check out COLOURlovers.com which breaks down interesting palettes by HTML color codes (you can also download as a palette for Photoshop, Illustrator, etc.). You can view the site's top palettes of the month. Color Inspiration from the Masters of Painting features palettes from Da Vinci, Picasso, Monet, etc. Other idea starters: Colors of the Top 20 Magazine Covers, Autumn, and Color in Science: Microscopic Photographs.
Related: Color Palette Generator lets you enter the URL of an image to get a color palette that matches the image. DigitalColor Meter, a built-in utility in Mac OS X, lets you identify the HTML colors of any image or screenshot on your computer. Happy color hunting!