Extensions for Youtube and Vimeo
This extension has been out there for a while and not actively developed but still kept up to date with latest LTS version of TYPO3. Gives good control over Vimeo videos and puts it into any responsive template.
Youtubevideo
Gives you full control over YouTube videos, with custom cover image and cover text.
Vimeovideo
Fully responsive Vimeo video content element. Includes back end preview in page module.