What's the most user friendly way to create a video block in a matrix field? I want to make it super easy for my user to embed a video from YouTube (maybe eventually from other sources) without having to get the iframe code. They should only have to enter the URL for the video, and maybe check a couple of optional settings, and the code will do the rest.

I'm planning to share the snippet and field architecture I develop here to save myself/others time in the future, but if someone else has already done this and wants to share first, even better!
From basic to robust:

Redactor has a plugin along that same vein but it's more basic—feed it a URL and it spits out the embed code in a Redactor field.

Craft-video-embed-utilty sounds like it might work as a basic option here. It's not a field type but a Twig filter that'll take the video URL the user enters (you could use it with any field, including a plain text field) and then spit out the necessary Twig embed code. If you want to build your own "options" from scratch, this could work.

Embedded Assets allows you to use embeddable media such as YouTube videos to your assets manager and spit out the embed code necessary. 

Dukt's premium Videos plugin is probably the most robust option. It'll actually connect to YouTube or Vimeo, hooks into Craft's interface, and visually allow you to search for and embed videos. It includes a videos field type that matrix compatible.