If you want the user to be able to type into the box then use a combobox e.g. if you had a combobox with Aaron, Ben, Dan, Paul in it. As soon as you typed P you can set the combobox to populate with Paul. You can also type entries that aren't in the combobox if the MatchRequired property is set to False. Comboboxes are also probably better for large lists.
If you are working with a relatively small list and don't want the user to type anything then use a listbox.
My personal preference would be a combobox.