Paramount is betting you do, and they've created a new channel on YouTube called the Paramount Vault, which features over 100 full-length feature films from their archives (though the features only seem to be available in the US at the moment). While a number of these are quite a bit older, with some science fiction B-movies thrown in for good measure, they also have an eclectic mix of newer films. Here's their intro video for a sense of what the Paramount Vault is all about:
As others have said, it's not clear if these films will always remain free on YouTube or if they will cycle them out as newer films are made available. It's also not clear when we might see the newest Paramount films on the Vault channel, though it's possible we may only ever get clips of many of them. It makes a lot of sense that they'd upload hard-to-find classics, but I'd be surprised if they uploaded a ton of the newest movies for any significant period of time (though you never know, as they must be banking on ad revenue paying for some of this). Either way, there's plenty to like, as they've got epics like the 5+ hour 1900 from Bernardo Bertolucci:
As well as some newer films like Noah Baumbach's Margot at the Wedding and Arie Posin's The Chumscrubber (both of which this author happened to enjoy the last time he saw them):
You can also take a gander at the first film from The Wachowski's called Bound:
I'm less familiar with some of the classics, though I'm sure plenty of you out there will give some of them a go. Their categories are a bit confusing at the moment, and it seems like some movies overlap in multiple categories, but I'm sure they will get that straightened out soon enough. If there is really anything to complain about, it's that it seems like these are just the standard definition DVD rips, so hopefully newer films get the high definition (or even 4K) treatment.
If you want to see what else is on the Paramount Vault, head on over to their YouTube channel.
Source: Paramount Vault