Draw.io is a free web application (with a few pay options) which can be used for mind maps, diagraming, flowcharts and more.
It works like Visio or Lucid chart, where the user drags items onto the canvas and then connects them. Once connected, they stay connected, and the objects can be moved or resized, depending on the needs of the user.
Diagrams can be exported in a multitude of formats, including png, and can be embedded in Google Sites or Google Docs documents.
As for pricing, draw.io is free for personal Google Drive accounts, Dropbox accounts, and Microsoft OneDrive accounts. Although draw.io does cost for Google Apps accounts, it is free academic domains and charitable use.