I think he died. If you want to think about the film purely like a computer, Neo was like a programme, there to get rid of the virus (Agent Smith), and balance all the things in the Matrix which had caused it to fail or go wrong in the past (eg putting the elements of love, compassion, and irrational and illogical human thought in). Lots of different versions of Neo had been created by the Matrix in the past, as you saw when he met the Creator. This version of Neo was the best designed, and completed his task, allowing the Matrix to reset itself, without all the problems, and therefore he ceased to exist (died). Just like the Key Maker died as soon as he got them through that door (he completed the task he was designed for, therefore ceased). In the same way, Trinity (who represents love), got Neo to a certain point and showed the power of love, then got killed cus she sort of fulfilled her role.
The film can obviously be interpreted on a million different levels. I know this explanation takes a very objective view, and interprets everything symbolically, but it can make sense. An article in Empire magazine sort of talked about the film like this, so it's one way of looking at it.
I think Neo's presence in the Matrix, as well as his physical body died.
Now, did anyone understand Donnie Darko.......