Here is a list of white label video providers that I have worked with:
When you used these services, you can upload video content and create players and playlists to embed in your site/blog. All these services scale their players for responsive web to mobile optimization.
With the three above mentioned services, you can insert pre-roll ads in front of the content if need be and all have analytics dashboards to assess viewership. I know that Brightcove has an Omniture Site Catalyst integration and I'm sure the other have an open API you can use to get your data into SiteCatalyst or possibly Google Analytics. In fact, I just checked and Kaltura has a plugin for Google Analytics with documentation here: http://knowledge.kaltura.com/google-analytics-kaltura-player.
Looks like Ooyala, our of Canada, is a competitor the above mentioned players.
You can also use a service like Vimeo, which has a premium tier as well, but you'd probably get better analytics out of a true hosted video platform than you would Vimeo, which may give you some basic analytics, but is not as robust. But, I could be wrong...you'd have to do a little investigating to find out.