To refresh a specific widget, click on the widget once, and hit Command + R.
You'll notice a very cool "swirl" effect, which almost looks like a hurricane on a radar screen:
Every widget you refresh will perform this "swirl" action, and subsequently refresh the widget content.
If you're wondering what widget this was that I refreshed, it's the basic weather widget from Apple:
If you manually click the "+" icon in the lower left corner of Dashboard view, your "widget toolbar" will appear along the bottom.
Here you can add or remove widgets from display.
To open this "widget toolbar," you can also hit Command + "+".
That's Command and the "+" key at the same time. Hitting it again will close the "widget toolbar."
This is not so much a keyboard shortcut, but a keyboard adjustment.
If you hold down the "Option" key while in Dashboard view, and hover over a widget, you can manually remove the widget by clicking the "X" in the upper left corner of the widget.
The "X" only appears when you move the mouse over each widget.
This is quicker than opening the "widget toolbar" first, and then removing.
Much like hitting Command + R refreshes a widget, hitting Command + I should provide info on the widget. (Only applicable for widgets that have a "back side" info panel.)