The über-Mac geeks over at mac geekery answer a reader question I have often wondered about myself: is it possible to hide an application's icon so it does not appear in your Dock, even though the application is running? And the answer is yes, if you're up for a little bit of relatively easy hacking. Apparently all you have to do is drill down into the Application package (right-click on the application icon and choose "show package contents") and add one key to its Info.plist file. JC warns that this may have some unintended consequences, as the "Dock controls almost all aspects of application switching," so if you do this you may "lose" the application and have no way to interact with it. In addition some applications "interact with their Dock icon programmatically" (e.g. the way Mail.app shows the number of unread messages in its Dock icon), so this is not a good idea for those programs. However, if you have something that must run all the time, but with which you don't interact much, and whose Dock icon you want out of there (e.g. the DynDNS Updater client), this is a handy tip. One word of warning, be sure to duplicate any application you decide to try this on first, so that you can go back if necessary. A second word of warning, this affects the menubar as well as the Dock.
[Update: several commenters have mentioned Dockless, as a more user-friendly way of doing this. I originally misunderstood what Dockless did, but after a little more research it turns out that Dockless basically just automates the very same process this tip describes (i.e. changing the value of the LSUIElement key in the info.plist file).]