Embed video on your post is a way to keep your visitor on your site, and it is always a great way to interact with your visitors. Thanks to all the WordPress developers, embedding media on WordPress post and page is getting a great improvement on every major update.
To embed a YouTube video, all you need is to place the YouTube URL, and you are done! The same goes with Vimeo.
WordPress support a wide range of video site for such embed way. Here are a few:
You can refer the full list here: http://codex.wordpress.org/Embeds
Note: Do you know that you can directly key in PhotoBucket image URL to embed that image?