The longest running play on Broadway is The Phantom of the Opera which as of today has had over 8,500 consecutive performances and is still ongoing. The second longest is Cats which had a total of 7,485 consecutive performances.
phantom of the opera...22 years and counting since Jan of 1988. On September 16, 2009, The Phantom of the Opera celebrated its 9,000th performance making it the longest running show in Broadway...
Currently Phantom of the Opera http://en.wikipedia.org/wiki/List_of_the_longest-running_Broadway_shows^the above link is a great list of the longest running musicals on broadway!