Discourse arguably the #1 forum on the web. It's open-source, fast, has a 1-click setup from digitalocean, heavily maintained, and reputable. It's intuitive and fluid - you can paste images directly in, all URLs have previews, and the extendability is beyond-imaginable.
They also support SSO, 3rd-party plugins/addons, boast a full API, and can do just about anything. It's extendable by any way you want it to be.
Here is an example of Discourse running:
More @ https://discourse.org