If you already have a Google account, you can upload videos to Google Photos/Picasa Web Albums and share the link. I've been backing up all my photos and videos there because it is now free unlimited storage for photos up to 16megapixels and videos up to 1080p. You can share a link or directly embed photos from there, but I haven't figured out how to embed the videos stored there yet. Google also owns You-tube I think and you can embed You-tube videos easily, so that all gets a little confusing. I think also that people with Amazon Prime get cloud storage included, but I don't know what that can do as far as sharing.
I put up a few videos on You-tube to try it a while ago, and it wasn't too bad. Not as simple as sharing pictures from my Google account, but doable. I think I'm the only one that ever looked at them though!
Here is one I have on You-tube embedded using the bb code tag, hopefully it works!