The crucial factor is whether the menu option requires additional information (input or a selection) before it carries out the operation. So Help-About doesn’t require an ellipsis, but File-Open does. That’s what the Microsoft, Apple and KDE guidelines say anyway.
Microsoft Windows applications are supposed to follow Microsoft’s “User Experience Guidelines”. Here’s what they say about ellipses on menu items.
While menu commands are used for
immediate actions, more information
might be needed to perform the action.
Indicate a command that needs
additional information (including a
confirmation) by adding an ellipsis at
the end of the label.This doesn’t mean you should use an
ellipsis whenever an action displays
another window—only when additional
information is required to perform the
action. For example, the commands
About, Advanced, Help, Options,
Properties, and Settings must display
another window when clicked, but don’t
require additional information from
the user. Therefore they don’t need
ellipses.
David’s answer cites the KDE 3 user interface guidelines,
Notice that every item in a menu that
first opens a dialog requiring
additional information must be
labelled with a trailing ellipsis
(…) (e.g. Save As…, Open…).
There’s no space between the menu item
and the “…”. A simple confirmation
dialog is not considered a dialog that
requires additional information.
The Apple Human Interface Guidelines say:
Append an ellipsis to a menu item’s label when people need to provide additional information before the action can complete. The ellipsis character (…) signals that another view will open in which people can input information or make choices.
Old versions of the HIG went into greater detail, and gave examples:
When it appears in the name of a
button or a menu item, an ellipsis
character (…) indicates to the user
that additional information is
required before the associated
operation can be performed.
Specifically, it prepares the user to
expect the appearance of a window or
dialog in which to make selections or
enter information before the command
executes. Because users expect instant
action from buttons and menu items (as
described in “Buttons” and “Menu
Behavior”), it’s especially important
to prepare them for this alternate
behavior by appropriately displaying
the ellipsis character.