There's another way, too. It's a little more technical, but, in my experience, it works much better than using the Get Info command.
1. Get or create a new icon (a .icns file). You can create a new icon from any artwork using Icon Composer which is part of the Developer Tools from Apple. It generally works best if your original artwork is square (so it doesn't get distorted when scaled to be an icon), larger than 128x128 (so the largest icon size doesn't look pixelated), and is in a format that has transparency such as .png (so your final icon isn't just a square). Save your new (found or composed) icon with the file name iTunes.icns.
2. Open the Applications folder and right-click (or control-click, or highlight then click the sprocket button in the window) on iTunes. Pull down to "Show Package Contents" and select it.
3. In the new window that opens up, open Contents, then open Resources.
4. If you want to save the original iTunes icon, find it in this folder and rename it to something like iTunes-old.icns. Then drag your new icon into this folder.
Done! When you launch iTunes again, the icon in the Dock will automatically update.
Here's my iTunes icon:
