Technically, no. YouTube’s Term of Service (ToS), for instance, states that users are not allowed to “access, reproduce, download, distribute, transmit, broadcast, display, license, alter, modify, or otherwise use any part of the Service or any Content except: a) as expressly authorized by the Service or b) with prior written permission from YouTube and, if applicable, the respective rights holders.”
However, it’s not illegal to download videos for personal use – just remember you hold no rights over the videos you’ve not created. Therefore, you should abstain from sharing them as your own with the intent to profit or distributing them in any other way.