Web browsers are notable for using this kind of interface, an approach pioneered by Opera and subsequently adopted by Mozilla and a number of others. Now, almost all web browsers except for Internet Explorer and OmniWeb support a TDI.
One important advantage of the tabbed document interface is that it holds many different documents logically under the one window, instead of holding a lot of small child windows, though, if too many documents are open, the tabs can be rather difficult to manage or label.
The major disadvantage is that you are restricted to viewing one window at a time, something which can be done with MDI.