He said the matter was closed, and that that should be an end to it.
The word 'that' is one of the only words I can think of that I dislike. There are so many instances where I'm not sure whether including the word is necessary or even gramatically correct. I tend to understand the concept behind doubling the word 'that', as in my quoted example. The second occurance of the word in this case is referring back to the previous sentence (or rather, the object or idea to which the speaker is referring to as being the last item being spoken about the matter).
I am trying to think up a simple sentence where the word 'that' can be used, but seems to make the exact same sense if you pull the word out. I come across these a lot when writing, but can't seem to invent one now. I bet this issue is dealt with in university English classes at some point :)