I guess the question boils down to whether you need to be in complete control of the video, and whether you have money to throw at the project. If you host on youtube etc you are subject to their terms of service and need to work within the constraints of their branding.
When I have needed complete control of Flash video clips for clients I have used the JW-FLV player. It will happily serve FLV files off an HTTP server. It is possible to embed the player in another Flash movie, but most often you will control the playlist from HTML links. Hosting video files can get very expensive, so expect to pay a hefty bandwidth bill.
I would use a 3rd party service if I was creating video for public consumption that had some sort of marketing aspect to it. Host it on YouTube and you can get very good exposure, and people have a chance of finding your video. These services also have global reach in their networks so you may get better performance worldwide.
Google recently released Video for Google Apps customers. This allows you to secure your Google video to users belonging to your organisation. This bridges the gap for some projects that would traditionally use self-hosting.