You tube is great because it's simple, easy, and cheap.
You don't have to pay for bandwidth if all of a sudden your clip goes viral and is watched by 2 million people around the world.
It's also another way that you can drive traffic to your site. Users will find your video on You Tube rather then only on your site, and with a few clever marketing addons you could redirect them back to your site (e.g. See a transcript of this video at www.mysite.com)
Have a look at the You Tube blog to find out all the features that you can include as part of your video also.
On the other hand, you're stuck with the way YouTube compresses your video, have size constraints and also have the limitation of the length of video.
You will also have the "You Tube" slapped across the video in a watermark, which depending on your audience might not be the best.
Also, at the end of your video a bunch of related videos will appear even when you're embedding on your site which could potentially drive traffic away from your site and your videos and back to youtube (there may be options to change this though).
You Tube isn't the only video hosting option, you should also check out Vimeo, Revver, MySpace Video, Google Videos, Grouper, Yahoo Videos,AOL Uncut Video, Dailymotion etc etc (search for video hosting)
I prefer Vimeo only because I'm more impressed with the final products I've seen from them, not because of personal experiences.
If you want to go the "host your own" then you don't need to look at any money at all (well apart from your own hosting fees and bandwidth).
Have a look at Long Tail Video which is a free player for your site, although if you're hosting on a CMS, for a Corporate site or you are making money from your site (listing ads) they do ask for a one off fee (nominal fee, about $30 at most).
Of course you still need to covert your files to FLV, and there are plenty of options out there however my pick would be FFMPEG that can be run from the command line.
By hosting the own you have COMPLETE control over what happens to the video, how it is displayed, bit rate, size, audio quality etc etc, however it is a little bit trickier to set up then you tube and you will have to cover the bandwidth costs.