In this article, I'll list which websites, social media, and platforms let users easily download the videos shared on posts on the website to your computer for free, without you needing to resort to a third-party video downloader.
Warning: being able to download a video for free doesn't give you the right to redistribute it (e.g. upload it somewhere). I'm not a lawyer, but I'm going to assume that you should be able to download the video for personal use, e.g. to watch it offline in your PC, without running into legal issues.
Right Click -> Save Video As...
The following websites use the <video> HTML tag and as such you can simply right click on the video to save it to your PC.
With Permission
Some websites can display an interface to let the public download videos posted by a creator if the creator consents to it, i.e. the creator has a choice to allow or disallow their video to be downloaded.
It's reasonable to assume that if an author has the power to let you download the video, and deliberately chose not to, it's because they don't want you to download their video.
Vimeo
Videos uploaded to Vimeo can be downloaded by clicking on a button if the uploader allows it, although this is limited to upper tiers of paying accounts.
Logged-in users can download videos from vimeo.com that are available for download by the video owner. Not all videos can be downloaded.
[...]
Free and Basic members cannot enable video downloads.
https://help.vimeo.com/hc/en-us/articles/29641627072017-Troubleshooting-I-don-t-see-a-download-button-on-a-video (accessed 2024-12-07)
For reference, I found a video that can be downloaded: [https://vimeo.com/805542]. You can find a button next to the like button (heart icon) to download it.
Observation: Vimeo supports creative commons, but CC-licensed videos can't be downloaded if they are uploaded by users on Free and Basic tiers.
TikTok
You can download videos posted on TikTok when the creator allows it. When a video can be downloaded, you can right click on it to display TikTok's custom context menu and then click "download." If you have ever seen a video with TikTok's watermark on it, it's because it was downloaded this way.
You can save TikTok videos and photos to your device for offline viewing and sharing if the post creator allows others to download their content
https://support.tiktok.com/en/using-tiktok/exploring-videos/video-downloads (accessed 2024-12-07)
You can download videos ("reels") posted on Instagram if the creator allows doesn't deny it, however this functionality is only available on smartphones. You can't download them from the website on your PC for some reason.
This feature isn't available on computers, but it is available on these devices. Select a device to learn more about this feature.
[Two buttons appear under the paragraph: "Android App Help" and "iPhone App Help".]
https://help.instagram.com/520831036611383/ (accessed 2024-12-07)
Anyone on Instagram can download your reels and share your reels, unless you change your reels download settings.
https://help.instagram.com/520831036611383/?cms_platform=android-app (accessed 2024-12-07)
Not Possible
For completeness, platforms where it's not possible to download a video for free.
Note: although Pinterest displays a download button, attempting to download a video will instead download the cover image (i.e. the thumbnail) of the video.
Requires Payment
Some platforms don't allow users to download videos for free, but will allow paying users to download the videos.
On Twitter, it seems it's possible to download a video if you are a paying user.
Contains DRM
Some platforms don't allow you to download videos in a standard format like MP4 or AVI that you can play in a typical video player even if you are a paying user. Instead, your "download" merely grants you the ability to watch the video offline through the platform's official application. This is an example of DRM, and it happens with audio platforms too, e.g. Spotify.
Youtube
On Youtube, you can download a video if you pay for Youtube Premium, but you can only watch the video through Youtube's proprietary application.