How to move windows between workspaces using the mouse?

You can always right-click the title bar of a window and select one of the following options.

Move to Workspace Right

_{This will move the window to the workspace on the right.}

Move to Workspace Left

_{This will move it to the workspace on the left. In my case, it is down due to Unity's workspace setup.}

In Unity (from 11.04 to 17.04)

Select "Move to Another Workspace"...

...and select the workspace you want the window to switch to

_{This will move it to the selected workspace.}

Invoking the Expose mode

1. Clicking on the Workspace Switcher icon in the launcher

   

2. Hitting Super + S

Now you only have to drag the window to the desired workspace.

Some applications (Google Chrome and Qt based programs) the normal right click does not show the move to choices but alt-right-click does.

GNOME Shell: Ubuntu 17.10+

On GNOME Shell (default on Ubuntu 17.10+) another way is using drag-and-drop on Activities overview:

1. Open the Activities overview (similar to expose mode).
2. Click and drag the window toward the right of the screen.
3. The workspace selector will appear.
4. Drop the window onto an empty workspace. This workspace now contains the window you have dropped, and a new empty workspace appears at the bottom of the workspace selector.

You can also move windows directly between workspaces.