I have just finished watching the last episode of Code Geass: Hanyaku no Lelouch... Since it is a highly popular anime in Japan, we would expect the producers to come up with an ending that would satisfy the majority. And there is it -- an ambiguous ending... So did Lelouch died?
In my opinion there won't be a definite conclusion as there is sufficient 'proofs' for both cases. If you want to think that Lelouch is died, of course, he is stabbed, there's a great loss of blood and no one helped him. Suzaku killed him, C.C was praying in the church, and both of them are crying. If Lelouch isn't about to die then why do they cry?
However, on the other hand, if Lelouch is really dead... It seems... Too easy. In addition, to satisfy the people who are looking forward to a happy ending, the producers provide enough 'evidence' to show that Lelouch is alive. Yes, I do know that Lelouch did not get the immorality code from King Charles, but if he is strong enough to activate geass in both eyes, and strong enough to geass even the "collective unconscious", then god knows what he couldn't do. Ultimately, he did say that he is "Zero, the man who creates miracles". From that episode we already know, nothing is what we expected. Lelouch managed to destroy King Charles, the one with the immortality seal, so why can't he be immortal with/without the immortality seal, is the seal even important? And those who watched the anime knows that the immortality part of geass has to be activated with their first death, so Lelouch probably won't expect himself to be alive actually. In addition, if Lelouch is dead, why can the hot-headed Orange be harvesting oranges? He would most likely be plotting means to avenge Lelouch's death already.
The most convincing clue from the ending, I believe, would be the part where C.C appeared. C.C appears to be talking to Lelouch, and many suspected the farmer is Lelouch, otherwise why would he cover his face as it seems quite easy to just draw an old man at the same time. Thus, we are allowed to think it might be Lelouch. This possibility is strengthened by C.C saying "Geass makes people lonely, but it isn't true for you, Lelouch" or something of the same idea. Remember, Geass makes people lonely for C.C as immortality made her suffered; she had no one who can accompany her throughout her lifetime, and people she likes will die before her. But now, while 'talking' to Lelouch, she's actually happy, in constrast to her crying in the church earlier. For C.C to be happy, we can said she either resigned to the fact the it would be better off with Lelouch gone, or we could said that she is happy as she has found company (remember Suzaku said both C.C and Lelouch are companions) as Lelouch is immortal like her, and that Lelouch has proved her wrong. Geass don't make people lonely, in fact, if Lelouch lives, he should be having a great time as he no longer have to deal with politics. However, as the world has seen his pretty face, he has to keep it covered at all times. Lastly, the paper crane as we all know belongs to Lelouch so how did it get into C.C's hand if Lelouch never pass it to her?
Remember, Lelouch said geass is like a wish, and crane symbolises a wish comes true, and if geass didn't make Lelouch lonely, then he should be alive.
Of course, it's up for interpretation, those who said that he's dead can't prove it, those who said that he's alive can't prove it either. There is a balance argument between the two resolutions. Of course, I go for the argument that Lelouch is alive.
To hold on to the future, one has to be alive and Lelouch does not have to redeem his sins with death. Ultimately, god judges people not by who they are, but who they have become.
All-in-all, the moral of the anime is... "All hail Lelouch! All hail thee future!" [I hope I can hold on to that... I hate the future actually, I like the past best].