There are some really bloated "YouTube enhancer" type add-ons that do it unreliably. This has been a problem for so long that it's pretty clear Google doesn't care and wants YouTube videos to auto-play against the user's wishes. They want to force you into using their UI rather than opening videos in new tabs.
If you're fine with downloading YouTube videos for playing locally, I've found 4K Video Downloader works well, at least under OS X. You'll wind up with plain H.264/AAC MPEG-4 files.
When i'm on youtube I like to open loads of tabs before going through each one later. With click to play for flash this wasn't a problem, but html5 will autoplay and get very annoying.
Is there a way around this?
Do you think Youtube would be for or against that (i.e. do they really want me opening more than one tab?)
I'm using "YouTube Auto Buffer & Auto HD" with Greasemonkey (there's an alternative to this on Chrome) and I guess it should work, also it's not bloated, just the stuff you need.