------
For some reason, the most memorable moment for me was when Caius Cosades makes you head of the blades on Morrowind, gives you your last orders, and leaves for Cyrodil (because of his addictions). I don't know why, but it was just a really great moment.
A close second would have to be when I met the emporer?/Tiber Septim? at the Ghost Gate before heading after sunder and keening and he gives me that coin. At first I didn't realize who he was until I came back and no one had seemed to notice him.