I am building a responsive mobile-driven, video-centric site in WordPress, and never really gave the Youtube videos (themselves) much thought. This plugin works very well at making them responsive. I only wish I could customize the default video size to my own dimensions (rather than the 8 or so options given).
The bonus to this plugin - that I wasn't expecting - was the speed. Often, WP plugins can slow down a pages load times. So thanks to the devs for making this one quick plugin that strips out unneeded data and keeping load times short.