Too many to list but download only happens if there is a download button. YouTube is very clear on that.
"You shall not download any Content unless you see a "download" or similar link displayed by YouTube on the Service for that Content. You shall not copy, reproduce, distribute, transmit, broadcast, display, sell, license, or otherwise exploit any Content for any other purposes without the prior written consent of YouTube or the respective licensors of the Content. YouTube and its licensors reserve all rights not expressly granted in and to the Service and the Content."
So playing Flash is done on most tablets. I hope you understand I can't list them all.
But here's a few at the office that are fine. Nexus and Transformer. We used a web search to install the player.
Do any of the current tablets play and download them? If so, which ones?