Simply look here: http://en.wikipedia.org/wiki/Comparison_of_internet_forum_software_(other) In the programming language column, just look at which ones say "Ruby". Those forums run on Ruby on Rails. Twitter is working on Ruby on Rails.
Ruby on Rails is a free web application framework designed to make web development faster, simpler and more efficient. Often shortened to Rails, or RoR, Ruby on Rails is written in the Ruby...
There are many free forum scripts. The most popular one by far is phpBB. MyBB is also free and similar to vbulletin. Vanilla is a popular light weight forum.