Is there a way to disable autoplay?

In the current form, there are no options, or menus to change any options for the Netflix Xbox 360 application related to autoplay, or anything else for that matter.

I would hope this is an oversight that will be fixed, because I didn't really want to start and play Hot in Cleveland and have it stuck in my Recently Watched section for eternity.

Call their hotline to complain and request to make the feature optional. I just did and had a great call with the customer service. They have received a lot of calls/feedback that is strongly against the feature, or at least strongly pushing to make it optional (toggle on/off). Customer service number: 1-866-579-7115

This can now be done but it must be done through the Netflix website itself (this is not available in apps for iOS, Xbox, FireTV, etc).

Go to account settings and then you'll find the auto-play option under playback settings. Here's a 2 minute video showing how to disable auto-play. And here's the official Netflix instructions for it.