By default, Ubuntu does not have a trashcan on the desktop. If you want one though, it's pretty easy to add:

1) You need to open the Gnome Configuration Editor. To do this hit Alt+F2 to get the Run Application dialog and enter gconf-editor as the application to run.

2) In the left-hand pane of the editor, go to apps -> nautilis -> desktop by opening the folders.

3) On the right-hand side, there will be entry called trash_icon_visible with an empty checkbox next to it. Check this box and you will get a trashcan icon on your desktop.

You'll also notice other checkboxes available here for doing things like showing the Documents, Networks, and other icons on your desktop.