The Neo4j Heroku Challenge is a series of projects showcasing the potential of Neo4j, a graph database, in various applications. The challenge invites developers to vote for their favorite project using Twitter or by adding star ratings on Gensen. Three winning projects will receive an iPad3, and the developer with the most votes will be declared the winner. The projects include Neography on Sinatra in Ruby, D3 Followers Visualizer, Flattr what?, Flavorwocky, Frosty Mug, Lightbulb, NeoBlog, Scala Plays with Neo4j, Graphtag, Neoflix, Node-Neo4j Template, Python, Flask, Neo4j Demo App, Neo4j Grails Demo, Neo4j or Bust, NeoQuote, and Scalatra Neo4j. These projects demonstrate the versatility of Neo4j in different programming languages and frameworks, such as Ruby, Python, Scala, and Clojure.