Can I put on my website a video that I downloaded from Youtube?

No you can't unless you either have written permission from YouTube or you use an embeddable player. From the YouTube Terms of Service.-http://www.youtube.com/static?gl=us&template=terms " 4. General Use of the Service—Permissions and Restrictions YouTube hereby grants you permission to access and use the Service as set forth in these Terms of Service, provided that: You agree not to distribute in any medium any part of the Service or the Content without YouTube's prior written authorization, unless YouTube makes available the means for such distribution through functionality offered by the Service (such as the Embeddable Player)."

Doing so is copyright infringement if you don't first obtain permission from the copyright holder. Up to a $150,000 fine per download and some jail time is what you would be looking at if the copyright holder pushed the issue. It's also a terrible waste of your time and effort. Youtube makes it trivial for you to embed the video in your page and does all the heavy work of hosting the video and formatting it for the device that's trying to play it back. There's no reason at all to not embrace the legal path.

If the video is present elsewhere with a download option and a clear redistribution permissions then you should be good, otherwise, you're violating more than one line: 1) Downloading videos from a site that doesn't allow downloads 2) redistributing a video (intellectual property) without proper rights. Having said that, what matters to most IP owners is whether you're making money off their content or not; in your case that would be advertising money coming in from video viewing traffic.

Unfortunately you are not able to download videos from YouTube unless you download a plugin from an outside source. The act of downloading videos from YouTube breaks their https://www.youtube.com/static?template=terms conditions. If you want to put a YouTube video on your website legally, simply embed the video and add it to your website. Embedding videos from YouTube is completely legal.