This isn't the first time I have experienced this feeling and I find myself longing for the days of owning DVD's. I don't want to pirate stuff, so what are my options now? I know that some services like Apple TV offer "ownership" which is fine but since they only have their own catalogues, I would need to have my collection scattered all over which I don't really care for. And even though the problem isn't near the same level when it comes to music (at least, not currently), I also really enjoy owning vinyl records and knowing that I have access to them even if the internet goes down etc.
So, I guess that Blue Ray is the best option? Is new stuff released on those? And do they last or should I expect discs to lose data after 8 years or something?
You'll want to use an uncompressed and unencrypted format. You might want multiple formats, in multiple places.
Likely one of these will be network attached storage with RAID, however it's been 10 years since I did anything like this so things may have moved on.
You may also want to think about ensuring you have players that can play the formats.
IIRC Blu-ray discs are expected to be OK for 15-30 years, however I don't know enough to say whether this is specific to certain manufacturers or usage.
From my limited knowledge, most content is still released on disc, however with the move towards streaming, I can foresee this may diminish over time. IIRC the Blu-ray market (both releases and players) is shrinking year-on-year.
I too have encountered an immense amount of frustration due to content rights being sold to a single provider, who is not one of the three or four we already subscribe to.
Why do you not want to pirate stuff? I personally use a VPN to torrent stuff, so my ISP doesn't send out a scare letter or cut my connection.