Screencast-o-Matic is an online, easy-to-use, screen recorder that works in your browser with no download required. It works for Windows, Mac, and Linux.
The free version gets you 15 min record time, upload to YouTube, and export to a variety of video formats. While the 15 min time limit may seem an issue, I've found for most things that is long enough. You can also purchase a Pro version for $9 / year that increases your record time to 60 min.
To use it, you simply click "start recording". It then loads a Java app and you can record your screen.
Please share any other screen recorders you like with us.
(thanks to @normgregory for sharing this resource)