Q. Can I stream Netflix or other streaming services in my classroom if I paid for the subscription?

Academic and Student Affairs has a guidance document about this for review in Word Document format. In summary, what is important to consider is: 

1. Copyright law and contract law are separate processes. When you subscribe to a streaming service, you will have a subscription agreement with a terms of use. By accepting the conditions of that agreement, you are accepting that you will follow said agreement. This essentially means that you may waive your right under copyright law, and instead have taken on the terms of a contract.
2. Review your terms of use/subscription agreement. Netflix, for example, typically says something along the lines of granting you permission to stream its collection for yourself and your household family members. This does not normally include classroom viewing.

Conversely, for streaming websites like YouTube or Vimeo, it will depend on the video. When considering showing a YouTube video, consider:

1. Is this a legal copy of this video? Does the uploader have the copyrights to upload it? If no, then you may not be protected under copyright law if you show it in the classroom.
2. If the uploader has the copyrights to the video, did you have to pay a subscription fee to watch it? For example, is it locked behind a paywall unless you pay for Youtube Premium?
3. If the video is lawfully uploaded and it is available for anyone to watch without a subscription, then streaming it in a classroom from that original source is not that much different from watching it alone. However, this does not necessarily give you the right to download a copy and distribute it! For that, additional permissions may be needed.
4. To make things more complex -- Netflix, for example, has its own YouTube channel where it sometimes uploads documentaries. These may not be available forever, if their own agreements with documentarians or other copyright holders change. In this instance, Netflix has chosen to make these available for anyone to view, presumably because they have the rights to do so. In this case then, the purpose is to allow for educational viewing without additional licenses.

In brief--it is not likely that a paid subscription service will permit you to stream videos in a classroom, but review the terms of agreement regardless. You may need to acquire a public performance/additional educational license. If you have a copy of a video that someone else paid the license for, check to see whether it was lawful for that copy to be distributed in the first place.