The current file size limit is 8mb. A useful tool for downloading streaming video from any site anywhere: https://addons.mozilla.org/en-US/firefox/addon/unplug/ (if someone knows a chrome alternative please post it so I can add it)
Windows: Use webm for retards or VLC to easily create webms from any video you want.
Currently removed from GitHub thanks to SJWs Webmbro (webm for retards, based on FFmpeg) - (scroll down on page) https://github.com/WebMBro/WebMConverter (updated version, advanced features: https://github.com/nixxquality/WebMConverter )Make sure to tick the sound option. Otherwise it's fairly self explanatory.
VLC - https://www.videolan.org/vlc/Use the built in record function. Here's a tutorial: http://www.cnet.com/how-to/how-to-create-video-clips-in-vlc/
Mac: Currently I only know of using ffmpeg with the command line to make new ones. Input would be greatly appreciated.
Linux: If you're running linux you'll want to use ffmpeg as well.
FFmpeg - https://www.ffmpeg.org/Instructions on how to use ffmpeg here: (somebody please find me a good tutorial. I'm finding a lot but it's all shit.)