It depends on factors such as privacy, cost of bandwidth (which relates to the amount of visitors) and formatting of videos suitable for web.
If it is your server, in theory, the files are under your custody, but this will entail costs with security, traffic, coding of the videos, installation of a media player on the site. And as well remembers the bfavaretto, "If you host on your server the browser makes a 'fake streaming''"
If you’re gonna use a hosting service for videos en, Traffic and coding are no problem, and the issue of privacy will vary depending on the service. On Youtube and Dailymotion, videos marked as private can only be accessed by other users of the service when logged in. YT has the option to leave the video unlisted and only those who have the URL can see, but just a Twitter with the link and it’s over. Vimeo Premium has the option to release playback only for certain domains and so you can leave the video behind a CMS for registered users.
The above Wikipedia article has some pretty cool tables comparing the various services. I separated those whose players are cross-platform (the links are to other articles on the Wiki, also in English):
blip.tv, Dacast, Dailymotion, Flickr, Internet Archive, Metacdn, Viddler, Vimeo, vzaar, Youku, Youtube.
{ Youku is in China, it’s an anthropological curiosity :) }
I’ve never used it, but I think it’s worth researching Hangouts on Google+. And finally, the Wiki.pt article for Media streaming is also interesting.
I mean, ideally I’m hiring a service to be making this available to me?
– Felipe
As I said, it depends. You will have to evaluate your resources and study the options of each service to be able to decide what is best.
– brasofilo
@Felipe If you host on your server the browser makes a "fake streaming". If the videos are long and you have a lot of people watching at the same time, you might not be able to serve everyone right. If you have how to hire a paid service to take care of encoding and streaming/band, is more tough.
– bfavaretto
This may be the case for hosting on a CDN. Large hosts usually support the creation of Cdns.
– Bacco
The CDN option is cool, yes, but it involves the whole issue of rendering and programming, a neat job. I used Vimeo $ on a video lessons site for the option to leave the video private and limit to a domain.
– brasofilo