There are many applications on your Mac that don't need a Dock icon. Having a Dock icon for applications that are accessed through a menu bar item or constantly run in the background would just waste space and clutter up your Dock. Many applications like this automatically hide their Dock icon (Google Notifier, Quicksilver) however some don't (Launchbar, HardwareGrowler).

Luckily, if it is a cocoa application, you can hide the Dock icon yourself. To see if it is possible, right-click (Control-click) on the application icon. If "Show Package Contents" is in the menu that appears, you can hide the icon in the Dock.

If this is the case, select "Show Package Contents" and look for the "Info.plist" file inside the Contents folder. Open this file using TextEdit by right-clicking on it and choosing "Open With - Other" from the menu.

In the file, paste the following two lines just after <dict> on the 6th line:

<key>LSUIElement</key>
<string>1</string>

Save the file and close it. For the changes to take effect, you need to move the application to the desktop and them back to its original location (OS X keeps a cache of the file, so you need to trick it into checking it again).

Now when you open the application, no icon will appear in the Dock. I wouldn't recommend doing this with your regular applications like iTunes and Safari as this also has the side-effect of disabling the menu bar. This means that you will have to quit the application using the keyboard shortcut Command-Q. If the application doesn't have any windows, you will have to quit it from Activity Monitor (in Applications/Utilities).

To bring back the Dock icon, simply open up the Info.plist file and remove the lines you added.

If you are too lazy to do this yourself, FoggyNoggin Software has created an application called Dock Dodger that automates the process.