Channel Videos is a great solution for simplifying the process of embedding videos for clients.It has a visual interface so that the client can see a thumbnail of the video prior to publishing. You can search videos by keyword from the CP or just add the Youtube url - which is a lot easier than customising the embed code and copy/pasting.
Additionally you can set the variables for the video height/width etc within your templates which will prevent the end user from embedding videos that are too large or too small - that's something you could not control with a copy/paste of the embed code.
And it supports both Youtube and Vimeo.