WebM is based on MKV, and it's been in browsers since 2010.
I've used MKV for lots of things, such as video production work, remuxing digital TV stream grabs so normal programs can play them, etc. It's the most reliable container format, from my point of view.
My whole media library of ripped DVDs and Blurays (that I legally own) is in MKV format. You get video, chapter marks, multiple audio streams, and subtitles all in one file. Plus almost every modern device plays them. I love it as a container format.
My MKVs typically have H264 video + AC3/DTS audio.