If you're going to publish videos inside of a membership site, You want those videos to be protected from people who are not customers. In most cases, using a good membership plug-in will prevent people from ever having access to your videos.

However, if your videos are hosted on a site like YouTube, then your members will be able to share the link to the video with their friends.

To prevent this, you need to host your videos on a different hosting service that allows you to restrict access to the people that are on your site and logged into your membership area.

Membership Site Solutions

Update: Since this video was filmed, I've changed the services that I personally use for my own membership sites. Here are the updated recommendations:

Wishlist Member (Wordpress)

If your website is already built on WordPress or is running on WordPress, then the WishList member plug-in is a good solution for creating a membership site. It allows you to restrict access to members.

Member Mouse (Wordpress)

Member Mouse is an easy-to-use plugin that you can use to turn your Wordpress website into a membership site. It's easy to set up using the included tutorial videos.

Hosting & Protecting Your Videos

Here are a few tools you can use to publish videos on your website or blog if you don't want to use YouTube. These solutions will essentially limit your video audience to people that are on your membership site:

Easy Video Suite - this is essentially a software tool that allows you to upload and host your videos on Amazon's S3 or Cloudfront storage and distribution platform. If you choose this option, I highly recommend optimizing your videos with Handbrake (or creating a free Wistia account to upload your videos and then download a smaller, optimized version of your video file). Unless cost is a serious issue, consider Vimeo Pro as an alternative.
Vimeo - Vimeo Pro gives you the ability to remove the Vimeo logo, sharing, etc. and allows you to restrict playback to your website or blog's domain (e.g. www.yourdomain.com)
Wistia - while more expensive, Wistia has a video player that loads quickly and they are very reliable. Wistia also gives you the option to restrict playback to your website or blog's domain.

Publish to Your Membership Site