Amazon's Video on Demand service is the closest thing to Netflix streaming that I've seen. So far, when I have checked periodically, Amazon's service seems to have less content available for streaming than Netflix; at least for items that are free to stream with a Prime membership. Most of the titles that I would have liked to stream were pay to play, but I know that they are expanding their selection.
No idea if it will ever come to Apple TV, but almost every other device supports it, including most connected TVs and Roku.