[Eruanna]

I think that the Rohirrim, being warriors, looked upon death as an 'occupational hazard' and that it was right and noble to make a 'good death'. Being the recipients of Eru's Gift meant that they believed that death was not the end, that there was a place for them beyond mortal life. The Elves on the other hand, being tied to the world, did not know what awaited them when Arda was no more.
This was one of the great differences between book and film for me. There was no indication of the different attitudes to death between Men and Elves. Book Elrond, as Lalwendë said is more concerned that Arwen is doomed to be forever sundered from her people, than he is with her eventual mortality. Film Elrond seems to view death as a 'punishment' for living a mortal life.
Perhaps, because I know the 'background' of the books, I did not find Theoden's death tragic. It seemed fitting that he had the chance to die with honour on the battlefield.
On the other hand, whenever I watch TTT, I am always very moved by the deaths of the Elves at Helm's Deep, Haldir in particular. His death seems tragic, after all he is meant to be 'immortal' yet he and the other Elves sacrifice themselves for mortals. I know that this is probably the reaction that PJ hoped to bring about; and with the music, the slow motion camera work and the actor's facial expression as he dies, he succeeds!