The Internet Archive is a great place to get legal source material. There is a neverending supply of great stuff there. You can find good material through Creative Commons Search as well.

If you are interested in fan-vidding or remixing pop culture footage you can use whatever footage you want regardless of who owns it if you follow the doctrine of "fair use". Obviously you can ignore the folks here suggesting paying for "rights" or using public domain or creative commons footage becuase the point of remixing is often to comment on or criticize current pop culture - and to do that you need to use bits of movies, pop songs and TV shows as your source material.

In fact downloading whole shows from bit torrent for a fair use remixing project can actually put you in a better legal position than ripping DVDs you may have bought becuase of the DMCA encryption law, though many vidders like the HD quality they can get from ripping their DVDs. Youtube footage is low-quality and does not make for good remixing source, unless its just not available anywhere else.

Here are some resources you might want to check out:

Video on how to make vids and remixes: http://www.technologyreview.com/video/?vid=420

For more on fair use, see the Center for Social Media website, they have a great PDF and video explaining the doctrine for online video creators.

For more about fan vidding check out the Organization for Transformative Works and FanLore.org

RebelliousPixels is right on. "Fair use" is a powerful argument for remixing popular culture. It's an important legal precedent so citizens can use media for satire, commentary, and debate.

Though as Shely says, "Fair Use" doesnt protect you from a huge corporation from suing you anyway. You would probably eventually win in court, but it would be a long process. Usually media companies simply send you a "cease and desist" letter. Court cases seem to happen if you choose to fight. But remember, I am not a lawyer.

All this being said, I have a good friend who remixes exercise videos. He finds old VHS tapes at yard sales, digitizes the VHS tapes, then makes fun videos from the crazy exercise craze.

Check out all Aaron's remix work at http://work.aaronvaldez.com/

I started compiling some of the sources, both legal and not, we've used for Wreck & Salvage videos http://delicious.com/wreckandsalvage/footage

If you want to keep it legal use Prelinger Archives and photos from Flickr using Creative Commons search parameters as Eric mentioned.

I think the easiest way to download youtube videos for remixing is by using keepHD (keephd.com)

If keephd is down or you need to download a video from a different streaming site, you can use the Firefox addon called Live HTTP headers (addons.mozilla.org/en-US/firefox/addon/3829) to find the direct url of a streaming video.

If all else fails and you really want to remix a video from a streaming website that doesn't provide downloads, you can use screencast software such as ScreenFlow (telestream.net/screen-flow/), but you'll sacrifice quality.

There are two factual copyright/fair use sources that I would encourage you and others to check out: The first is Code of Best Practices for Online Video: Remix Culture Fair Use Is Your Friend. This might help with the anxiety about using other content.

http://www.centerforsocialmedia.org/resources/publications/fair_use_in_online_video

You can also download a copy of the .pdf version as well.

There is also from the Center in the Study of Public Domain a comic book version about Fair Use, the right to re-use content and what independent video folks need to know.

http://www.law.duke.edu/cspd/comics/digital.php

There are copyright concerns with downloading clips off YouTube or downloading whole shows. If you do this, in order to avoid legal problems, you should get formal permissions from the rights holders of any of the material you use. This can be an expensive and complicated process, especially if music is involved with the clips. Some alternatives are footage licensing companies, rights-free/sharing collections or public domain material, if you can find it.

While it's less than legal, you can rip videos off of YouTube with a JavaScript bookmarklet. (Techcrunch offers one, for example.)

From there, you may need to convert the video into a more NLE-friendly format. I prefer Transcoder Redux:

http://www.techspansion.com/

Try this freeware: StreamTransport, The app is able to browse and download video clips from video hosting websites of HTTP, RTMP, RTMPT, RTMPE, RTMPTE protocol, and these cover overwhelming majority of websites such as Hulu, Veoh, Joost, YouTube, Yahoo Video, CBS, etc. Here is the link: http://www.streamtransport.com/