If a YouTube/Vimeo etc video includes the embed feature, is it legal to embed it on my website without first having contacted the video creator for permission to use it? Also, do I have to link/provide contact details on my website to the video creator having embedded their video?
Current EU law appears to be that embedding does not constitue copyright infringement of the video, even if the posting of the video to YouTube or Vimeo itself constitutes an act of infringement. However, the video must be freely available for this exception to apply. For details, see:
But NB the caution in the IPKat report: "... it remains questionable whether embedding copyrighted videos would never be tantamount to copyright infringement".
IPKat goes on: "Above all, it seems that the BestWater case has left one issue unaddressed, namely whether it is a communication to the public within the meaning of Article 3(1) of the InfoSoc Directive if a third-party work has been made available to the public without permission. Internet users could still be in hot water if they embedded copyright-protected videos from other websites, for example YouTube, if such videos were made available to the public without permission from the copyright holder. Further, embedding copyright-protected videos would be an infringement if the work concerned was directed at a new public, eg if the source video requires a login or other technological measures designed to prevent or restrict acts which are not authorised by the rightholder."
It seems to me that, notwithstanding Bestwater, embedding infringing videos (esp knowingly) does present some risks.
(I'm assuming here that your concern is with videos which have copyright problems, rather than those that are properly licensed to YouTube for the purpose of embedding.)
Of course, outside the EU different rules will apply.