one of my favorite being the exchange between Boromir and his father concerning the ring as well as Boromir's brother Faramir.
it showed Boromir in a much different light and made him seem like less of an ass. Plus it sheds a bit more light on Faramir and explains why he does what he does to Frodo.
of course you have to see it for yourself. but its such a shame that it wasnt included on the theatrical.