I uploaded my first video in late 2005, it's still up there.
I remember Google video was up around that time, and IIRC, the only true competitor. It should be mentioned that back then, the only ting that mattered to me was whether or not you could upload videos, and the site had a video player.
Pre-2005, I can honestly only remember downloading video files directly off websites, and then play them with some video player. I think I used Opera back then, and I think Opera supported some video players - but it was a real hassle, with the different video formats.
I also remember that before youtube etc., unless you had your own server or paid hosting, we'd use our "free" 5/10/15 MB hosting that came your ISP gave you, or other hosting sites provided (they'd usually have some free tier with a couple of free megs).
What we did, was to sign up for multiple such sites, so that we'd in effect get like 100/200 megs of hosting. Sometimes we'd have to chop up the files into multiple zip files, and distribute them over those websites.
Unfortunately, a lot of these smaller hosting sites disappeared over the years, and a lot of files got lost forever.
But yeah, when youtube etc. hit the scene, it was pretty much an overnight revolution. All the pains of sharing / hosting videos were gone.