Here's a neat trick: You can use the new Basecamp Mobile UI as a Fluid menu bar app on your computer. That way you can get a quick view of your Basecamp projects straight from your menu bar.
To set it up, you'll first need Fluid. Fluid lets you create a Site Specific Browser (SSB) out of any website or web application, effectively turning your favorite web apps into desktop apps. Download it and then make an app for this url: https://youraccount.basecamphq.com/mobile/ (replacing the italic part with your account name).
Then launch the app and choose "Convert to menu item."
Now you can access your projects right from your menu bar!
