I like movies like Amadeus, Downfall, Babel, Schindler's List, Life is Beautiful, Gandhi, The Lives of Others, The Pianist, Ray, The Lord of the Rings, Terms of Endearment, Gran Torino, Frost/Nixon, etc.
I'd like a TV series that is in the same vein as my taste in movies. Good acting, good music, good story, good cinematography. Those are some of the most important elements. I also like drama, intensity and tragedy. And I have a hard time following some movies and TV shows, so the plot shouldn't be too weighed down by tiny details that must be paid attention to in order to understand what's going on.
Also, it would be nice if the series were available on iTunes, but I realize that that might be a bit of a stretch.