I really only like the idea of a "tip of the day" if it is displayed when I can't do anything else anyway. For example, when the program is loading a large file. Suppose it has to load some large amount of data when the program is first started. Along with the "loading" splash screen, show a small tip, and have it disappear when the program starts. It's simple, unobtrusive, and can sometimes be very helpful to some users.
I hate to bring up "World of Warcraft" as an example in a programming discussion, but it uses this technique when you first login. Here is an example loading screen. Along with the loading bar and a full screen piece of art, it displays a small tip at the bottom of the screen. Usually these tips lead users to things they can explore further (such as a settings window, character customization tools, etcetera). For example, "Pressing ESCAPE will bring up a menu that lets you customize the the look and feel of the game".
Above all else: allow the user to easily close the tips and stop them from appearing each time. Make every key close the tip dialog when pressed. Have two buttons: "Close Tip" and "Close Tip and Never Show Again", or something to that effect.
