My mother-in-law has a cousin she likes to talk to. Because I like to simplify my tech support requirements by standardizing my entire family on a single platform when possible, all of my immediate family uses Google Hangouts (promoting saving money through free phone calls to the US and Canada also helps). Unfortunately my mother-in-law's cousin is on Yahoo and Skype and is not that tech-savvy. That means I want a video chat solution that is dead-simple and doesn't require a common account (if she had a Google account then my mother-in-law could just email a link to a hangout and just reuse that hangout every time).
Luckily it turns out that you can overcome these obstacles thanks to WebRTC. If you don't happen to know what WebRTC is, think of it as providing real-time voice and video in the browser without plug-ins. On a more technical level, think of it as browser-supported session and signaling support for voice and video communication. It's currently supported in Chrome, Firefox, and Opera (including Chrome and Firefox for Android); Safari and IE don't support WebRTC natively at the moment, but do have plugins (IE has announced plans to add support in the future). All of this means that you can now do video chats through the browser without installing a plug-in.
The common format is a website that will launch a video chat room at some URL (sometimes of your own choosing by picking a chat room name). You can then send that URL to other people that they visit in a supported browser. At that point all they have to do is allow the web page to access their microphone and camera (probably saying "look for something asking if the web page can use the camera and microphone at the top or bottom of the page" should be enough instruction for most people). The sites that I found which worked in some form from Android on Chrome are appear.in, Talky, and vLine, although none of them are mobile or tablet-optimized (Talky is my personal favourite). Mozilla is also adding support through Hello which requires Firefox to initiate the video chat but which can be joined through an WebRTC-supported browser.
And for you developers out there, a lot of open source code exists to facilitate using WebRTC, so if you want to add audio/video support to your own web page it shouldn't be too difficult.
So for those instances where you and someone you want to video chat with don't have a common messaging platform, WebRTC works out well as a common denominator.