[UPDATE: Adobe has discontinued the free Strobe player]
There are third-party applications that will play Flash video files, but those require installation — and that is often not allowed on shared or corporate computers.
One quick down-and-dirty option is to play the video in the browser instead. To do this, you can pass in a video name through SWF embed code to play any video using a generic video player SWF.
One good prebuilt player is Flash Media Playback. It is hosted by Adobe, so you don’t need to upload anything except the video file to your web server. You can configure it using this wizard:
You can copy and paste the embed code and place in any web page.
If you want to link directly to a video player that loads your video without embedding it into a webpage, you can pass in the video name and other attributes as variables along with the Flash Media Playback SWF URL, like this:
This will load the SWF and play whatever video you specify in the URL, and you can pass in any other supported variables along with it as well (see the Flash Media Playback docs for more info). In addition to standard progressive delivery, this will also work with any Flash supported delivery method such as live RTMP streaming or HTTP Dynamic Streaming.