It varies in time with each service in my experience, BluRay could become available for rent (or a HD streaming) still....now, as to wanting to watch a particular movie at a particular time in the format you want at that moment, that can be tough for a renter but your best chances in this regard I think are with Netflix (and I just checked, Blue Jasmine is avail on BluRay but not streaming).
"I realize that somebody playing free music isn't as commercial as a hamburger stand. But is it because you can eat a hamburger and hold it in your hand and you can't do that with music? Is it too free to control?" - Don Van Vliet (aka Captain Beefheart) discussing commercial success in the music biz