"Me three" re: Amazon Prime videos. Netflix and Hulu work wonderfully. We only occasionally watch something on Amazon Prime and I don't think there's been one time that we didn't have an issue with it (and I have fiber at home, 50x25 Mbps, and my ISP is well-connected network-wise).
I also blame Amazon. I only have 15mbps down, but Netflix never has a problem after it initially buffers. Amazon almost always has a few buffering periods throughout a video.