There are a number of ways to download a media file and play it at the same time.
mplayer http://www.path/to/file.avi -dumpstream -dumpfile out.avi & mplayer out.avi
You'll have out.avi
and play it as it downloads.
Or stream it to a named pipe. (example)
mplayer http://path/to/file.avi -dumpstream -dumpfile foo.fifo
cat foo.fifo | mplayer -
Depends on what you are watching. If you want to watch youtube without waiting for download or flash
mplayer -cookies -cookies-file /tmp/cookie.txt $(youtube-dl -g --cookies /tmp/cookie.txt "http://www.youtube.com/watch?v=video no. goes here")
You don't say what player you are using.