There are some useful comments at
http://www.imdb.com/title/tt1067086/usercomments, and I'd also like to add a few words.
I wonder whether it is really so or whether it only seems to me, but the way I see TK’s Chiba prompts me the following interpretation:
On the one hand, shinigamis are immortal themselves (at least there was nothing in the film to suggest the opposite), but this is a doubtful blessing – just remember the limbo where TK’s character and his dog have to spend their time in between ‘missions’. It’s a dreary grey space where nothing happens, where nothing diverts the eye, where the time stands still. I wonder whether shinigamis find this space restful, or boring, or maybe just treat it with no emotion – but (once again, it is very subjective) it seems to me that TK’s character finds it a lonely place, or at least grows to find it a lonely place, and not a very ‘justified’ place for him to be in, to that. What I mean is he played a shinigami that evolves, changes, becomes more and more human (just look at his mimics, listen to his intonation when he’s speaking). What I see is his silent revolt against this limbo, and a sad reconciliation to the facts – to each his own, a human being gets a shortish earthly life full of emotion, mistakes, discoveries, and a shinigami gets his sad uneventful immortality. It looks as if somebody has robbed the shinigamis of something very important that Chiba begins to feel and to look for. At the same time he knows he’ll never be able to break through this fabric of his destiny.
Actually I see the film not as a chain of interconnected episodes, and not as the life story of the girl who rises from an ordinary girl of the crowd to a celebrity and then sinks into oblivion again, gaining maturity and understanding of things. I see the film as two major stories (the girl’s and the shinigami’s) that, though they develop along different lines, lead the viewer to the same conclusion. What really matters is the ability to understand, to love, to forgive, to look at the world with one’s eyes and mind open, to care, to be thankful to life for all the challenges it presented, to hope. Just remember the scene where she and Chiba are standing and looking at the peaceful sunlit landscape – it needs no words, it’s like an awakening (satori?). I think it is not by chance that at this particular moment Chiba finally sees the sun he longed for, for him it’s like a short but a very meaningful breakthrough, moment of freedom.