This question has shown up in the Bathroom a bunch lately and I've answered it each time, so this time I'm going to make the post permanent.
This will work for more than just videos from YouTube, but you will have to experiment with the other video sites. First thing you will need is a .flv viewer. The file extension .flv stands for Flash Video which is the second most popular video format on the web, it also happens to be the format that YouTube, ABC, CBS etc use. For a lightweight player that works on both MAC and PC, try this:
http://www.wimpyplayer.com/products/...lv_player.html
It works well and is pretty small and easy to use. Adobe will be coming out with their own player in the future, but for now, you can use this puppy.
In any case, go to YouTube and go to the page with the video you want to capture. For this example, I will use a NightCat (Ross) video because he is the man, the myth and the legend. When you have selected the video, you need to copy the URL address at the top (highlight the address and press CTRL + C):
Next, go to a website called KeepVid:
http://www.keepvid.com
In the top box, you want to paste the address you just copied and then click the download button:
Once you click the Download button, the KeepVid page will expand a little bit and give you something that looks like this:
Click the link that says "Download Link". You will then get a window that looks like this:
Click the "Save" button. When you do, you will get a save dialog window. In the filename box, you want to change "get_video" to a filename that describes the video and add a ".flv" at the end of the filename. I have done this in the next screen capture (I named the file Nightcat Flower Bottle Stopper.flv):
Save the file to any location that you like. It could take several minutes to download it depending on the size of the video. You now have the flash video file on your system to view. Open up the Wimpy Flash Video viewer that you downloaded earlier (or for you techy types, use whatever viewer you like.) Open the file you just saved and enjoy the show! You can now burn the video to a DVD for archival. To burn for watching on a regular TV/DVD player requires more software and technology skill that can get pretty in depth and is out of scope for this tutorial (it also can get pretty complex.)
Anyway, I hope this helps!