How to Download YouTube Videos

When the topic of downloading YouTube videos comes up, there's a side subject that must be broached: Is it legal? When it comes to copyright, as long as you're downloading a video for your own personal offline use, you're probably okay.

It's more black and white when you consider Google's terms of service for YouTube, which reads: "You shall not download any Content unless you see a 'download' or similar link displayed by YouTube on the Service for that Content."
After all, watching YouTube videos offline is taking money out of Google's pocket and those of the videos' creators. There's a reason YouTube runs pre-roll ads: people make a living that way.
So, let's be clear, taking video from YouTube is a big no-no. If you want to share a video, YouTube makes it pretty damn easy to do, from embedding to emailing to sharing via social networks. You don't really need to download a video most of the time. But maybe you have your reasons. We won't judge. If you must download a YouTube video—absolutely need to, just for yourself, and not for dissemination, and not to be a total douche-nozzle—here's how.
[Note: This story is updated frequently as the tools involved change regularly. Some of those changes are not always pleasant, such as software so full of "extras" it gets flagged as malware by antivirus tools. Th same goes for the helper websites—a change in the advertising network used by the site can also create issues with malware. The programs, services, and sites in this story are all working spam/virus/problem free as of this writing, but caveat emptor. Big time. Especially if you're not really emptor-ing.]

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Software

Third-party software is where many will find the best control for downloading online videos. Typically, you paste the URL for the YouTube video you want into the app, and it downloads the highest quality version it can find, typically in MP4 format. (It used to be that YouTube videos were all Flash-based, so your download was an FLV file, but those tend to be harder to play back. MP4, short for MPEG-4 Part 14 multimedia format, plays everywhere on anything.) Here are some options:
4K Video Downloader
Free;
4K Video Downloader (and companion app 4K YouTube to MP3) is frequently updated and features clear download links; no ad traps here. It does what it advertises: grabs videos up to 4K in quality and downloads to plenty of formats—it will even grab subtitles. You can even use it to download an entire subscribed YouTube channel. The sites supported are more limited to the big names like YouTube, Vimeo, and Facebook, but that probably covers most of what you need.

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Freemake Video Downloader
Free (with caveats);
Freemake claims it can download video from over 10,000 sites; "Loved by 83 Million users," it brags. With YouTube videos, it grabs things in any format, lets you save links, and downloads multiple videos at once. It also claims to be the fastest, grabbing a two-hour HD video in four minutes, but users can limit the speed if they're on a throttled internet connection. And that price? For free, it's a no-brainer, though you have to put up with advertisements. If you only want to grab music out of the videos you watch, it also offers the free Freemake YouTube to MP3 Boom.
The caveats: Freemake throws in extras when you install, including a third-party antivirus program and a forced change to Yahoo as your search engine in all your browsers. Make sure with this, or any program, that you do the custom install to avoid unwanted changes to your system. Should you trust Freemake? It devotes an entire webpage to reasons why you should—it claims antivirus programs flag them as a false-positive caused by its advertising partner installing potentially unwanted programs, but whether you believe is up to you.