Partly this is because of the viewpoint character being a young woman, Hitler's secretary Traudl Junge. She and Eva Braun and the other women of the bunker tend to be background figures in the standard historical accounts. By foregrounding their stories, Der Untergang makes this a story about human beings rather than about politics - certainly, human beings in an insane and deadly situation which is of their own making, but it makes the whole thing very watchable. (Having said that, I share strange_complex's dissatisfaction with the ending, for much the same reasons.)
The other superb thing about the film is Bruno Ganz's performance in the key role, a completely gripping and convincing portrayal. One point that struck me especially was his accent - as pointed out a while back by rcfinch, it is actually pretty harsh, a clipped mock-demotic contrast to the more mellifluous Hochdeutsch of the rest of the cast. It is an exaggeration - I tracked down some original recordings on Youtube to compare - but it helps enormously to convey the character - the abbreviated but intense vowels a metaphor for his career.
Indeed, more generally I found the film particularly shocking and direct because it was in German, not a translation. German is the foreign language in which I am best qualified (A-level) and for me it is a medium of well-meaning academic articles, great and less great literature and (in my later teenage years) occasional flirtation. I was never especially interested in war films, so never particularly subscribed to those stereotypes. But Der Untergang puts it right in your face: this language which I use for ordering food and drink when I change planes in Vienna is also the language of genocide and total war.
I understand that there are several versions of the English sub-titles out there, which is just as well - the ones I was watching with occasionally missed catching important nuances and inexplicably omitted entire lines (an early crack about the Asiatic hordes, a later report that they could hold out for only twenty hours). Unfortunately I am not quite brave enough to watch it without them.