What websites can be used in oEmbed?

Embedly currently has the largest curated list that I have found for what URLs are supported using the oEmbed standard. 

Note that not every URL will work inside oEmbed. For example, with Instagram you can embed a single post's url. However, you cannot embed your profile url. Twitter on the other hand allows for both!

The curated list from embody gives example URLs from each service so that you can see what is supported with that website. 

If you are trying to embed a widget that is not on that list, search around the services's website or email them to see if they support oEmbed.