I wouldn't call those singularity movies.

Maybe movies with transhuman/posthuman themes, but the singularity implies things about the rate of technological progress - certainly there wasn't much rapid progress in Terminator after the machines nuked the earth (except, maybe, in the production of new terminator robots, but even that wasn't fast, really).

Eagle Eye was a singularity movie in potential, but in essence it was no different than War Games in that it was about a rampant AI with no progression beyond. I, Robot had a far greater display of the advance of technology than virtually any Sci-Fi movie (except maybe the bicentennial man) and only displayed ~3 generations of robots (the replaced, the being replaced and the new) but is in no sense a singularity movie.

I doubt we'll ever see a movie truly depict the singularity in any way other than a glimpse and will be akin to virtually any sci-fi movie in any setting. We might get there with a great TV series, but that's doubtful.

IMO a singularity TV series would have to take the story progression of Taken in the generation skipping, but instead of giant leaps, it would be a leap of decades, years and then months as technology advances up to the '2030' mark.

For movies we'll be stuck with a BS intro that pails in comparison to the introduction of each Fallout game but will inevitably be describing similar events.

None of those present god (little g) level AI being created by humans but, AI (2001) is fairly close to the idea. By the end of the movie the robots knew how to bring someone back from the dead for a day and who knows what else.