Is there an easy way to rearrange or move the icons in the Unity launcher?

Click and hold the application's launcher icon, and then drag it up or down.

How to rearrange icons in Unity Launcher?

Just drag the icon out of the Launcher.

And then just drop it back in the Launcher anywhere you want.

In Ubuntu 11.10, dragging to the right didn't work for me. When I click an icon and hold the mouse button down for one second without moving the mouse, the icon drops down a few pixels. After that, I can drag it up or down the list to change its position.