There are a few different icons that are associated with a widget. Each widget will have a thumbnail image that displays in the My Widgets panel. Widgets that are displayed in a view will have an icon associated with that view. Finally, if a widget is published to a widget catalog, the widget document can specify a thumbnail image.

Thumbnail:
The thumbnail image used in the My Widgets panel is specified in the xml of the widget definition using the imageUrl attribute:
For Google Gadget widgets, the thumbnail defined in the gadget definition is used as the widget thumbnail. If that thumbnail cannot be found the 'toolbox' image is used.
For Web and Feed widgets, the favicon (http://server/favicon.ico) for the web site is used. If the favicon cannot be found, a default 'toolbox' image is used -> .
For Notes widgets (Form, XPage, Document, View), the imageUrl attribute is empty and a default Notes image is used for the widget thumbnail -> .
For Provisioning (Feature and Plug-in) widgets, the imageUrl attribute is empty and a default plug-in image is used for the widget thumbnail -> .
For Composite Application widgets, the imageUrl attribute is empty and a default application image is used for the widget thumbnail -> .

If you want to customize the thumbnail of a widget, you can export the widget, modify the imageUrl attribute and re-import the widget.

View Icon:
The view icon used for widgets that display in a view can also be customized (as of 8.5.2). The view icon used in the My Widgets panel is specified in the xml of the widget definition using the viewImageUrl attribute:
For Google Gadget widgets, the default view icon is as displayed here:
Opened in a Tab ->
Opened in a New Window ->
Opened in a Sidebar Panel ->
For Web widgets, the default view icon is .
For Feed widgets, the default view icon is .
For Notes widgets (Form, XPage, Document, View), the default view icon is . If your database has a default icon, the view icon will switch to the database icon after it is opened.

If you want to customize the view icon of a widget, you can export the widget, modify the viewImageUrl attribute and re-import the widget.

Catalog Thumbnail:
When a widget is added to a Widget Catalog, you can specify an image to use as the thumbnail that displays in the widget document. This image is not tied to the imageUrl attribute of the widget xml. So editing the thumbnail in the widget document will not edit the thumbnail in the widget xml.