The way we sort of do it is to use an normal button edit box and when the user clicks the button we present a separate form (which can be made to look like a drop down box if you like) with a checklist or listview with checkboxes enabled or similar. The user selects any number of the items then when the form closes we take the list of selected items and present them in the edit as a comma or semi-colon separated list. The edit itself is read-only so all interaction goes through the separate form.
But - I really don't like the whole approach (for our app) as it doesn't look good when you have many selected items and I'm looking to find a better way of showing the selection! I suppose one option is to use a read-only memo with scrollbars to show the items.
TMS has some nice components, one of which is the TCheckListEdit which might be of use.