If you want them to be able to download the videos you can get up to 50GB free hosting on Dropbox if you just do a couple of simple tasks like link it to extra devices. I think I installed it on just my phone, laptop, and desktop and got 50.
Also you can set Youtube videos to be private and only viewable if you directly link someone to it.
Edit: turns out I got to 50 because of a Samsung+Dropbox promotion so you could probably only get that if you had a samsung smartphone. You can earn free bonus space by doing stuff like linking it to twitter, facebook, referring people though. You can get a 100GB box for $8.25 a month, probably cheaper than paying for more hosting space from the website place but I don't know.