Umm... there are about 100 services that will rent/sell you a movie online. I use Amazon for all my movie rental needs. Works great.
For a real film buff being able to go rent F. W. Murnau's "Noseferatu", Michelangelo Antonioni's "Blowup" or Polanski's "Knife in the Water" was really important to me and something I took for granted. Almost every large city had a least one such film nerd rental place. And now that video stores are gone there's just a void for so much of this content.
One beacon of hope though which is supposed to launch soon is a streaming venture by TCM and The Criterion Collection:
I am really forward to this that and I hope its huge success.
https://www.amazon.com/Nosferatu-Silent-Max-Schreck/dp/B001O...
https://www.amazon.com/Blowup-Vanessa-Redgrave/dp/B000I157KO
https://www.amazon.com/Knife-Water-Leon-Niemczyk/dp/B004D22R...
Amazon + Netflix + Blueray player has become my perfect combination. The few titles that I can't get streaming I just buy the discs.
Make sure you try it first with a free or test movie before buying.
Noseferatu: https://play.google.com/store/movies/details/Nosferatu_The_V...
Blowup: https://play.google.com/store/movies/details/Blowup?id=5esCY...
Knife in the water: https://play.google.com/store/movies/details/Knife_in_the_Wa...
I prefer Google to the Amazon option. Much better device support (it works on pretty much every device out there) and the overall UI is just fantastic.