Pirating of DVDs and CDs is still quite common amongst Christians - at least in my experience. And I don't like it. I've heard lots of excuses for this - "software is just so expensive", or "music companies charge too much for their music", but the law (and the Bible) is clear that piracy is a no-go zone. As Romans 13 explains, we are to submit ourselves to the governing authorities, regardless of how inconvenient this might be. According to their website, there are two situations where you can download YouTube videos:
YouTube explains that:
"Except for the cases mentioned above, the YouTube's video player is designed to be used within your browser as an Internet experience."
"Content on the Website is provided to you AS IS for your information and personal use only and may not be downloaded, copied, reproduced, distributed, transmitted, broadcast, displayed, sold, licensed, or otherwise exploited for any other purposes whatsoever without the prior written consent of the respective owners."
UPDATE - 11 APRIL 2012
"Content is provided to you AS IS. You may access Content for your information and personal use solely as intended through the provided functionality of the Service and as permitted under these Terms of Service. You shall not download any Content unless you see a “download” or similar link displayed by YouTube on the Service for that Content."
"...it is actually illegal to play this kind of thing [YouTube videos] in a church service or public space unless you have written authorisation from the ORGINAL copywright holder Which means if people who put together videos for youtube sample vision or sound from somewhere else you need their expressed written permission. CCLI who give licence for music offer video licence for most major movies which gives you rights to play a clip for a sermon. Outside of this, if you don’t know created the video or don’t have their express permission as copyright holders it is breaking many interlectual property laws and could break a small churches bank totally as fines for this kinda things are massive."