Nope, I just download everything that I really like. Storage is cheap.
But when choosing what to save or not, I do apply some criteria:
* Popular / obscure? Obscure stuff may disappear easily. Popular stuff will be online somewhere.
* Freely available, or paywalled content? (how easy to obtain)
* Recently released, or 'oldie'? See above.
* Storage space (+ download time!). I'll be much more critical about saving a multi-GB BluRay rip than some funny pics, a few-hundred KB pdf or game dump for 30y old console.
* An educated guess about whether I'll ever want to use it again.
So what I end up saving, tends to be on the smaller side, sometimes difficult-to-find-online, and with 'replay value' (broadly defined).
Watch once & forget movie -> delete. I don't want to devote brain cells (now, or in future) on stuff that isn't worth revisiting.
I found that the wayback machine is really useful to get the title of the video, especially for songs.