The deal we got was for every 8 cabins, with a minimum of 2 people booked per cabin, we received one free berth. Note it's a berth, not a cabin, so you basically booked 16 people in 8 rooms and paid for 15. The TA gave us some other perks but this was the deal from Carnival. Not great but not horrible.
A Bad Day At Sea [with power] Always Beats A Good Day At Work
Carnival: Glory 2004, Destiny 2008, Splendor 2009, Freedom 2011, Valor 2012, Dream 2013
Celebrity: Summit 2011
Princess: Ruby 2010, 2014, Caribbean 2013, Coral 2014
As mentioned above, you will need 8 cabins to get the free berth but if group amenity points are available on the sailing you want, it usually only takes 5 cabins to get the group amenity (i.e. onboard credit, wine, etc.)
NCL Sun, Oasis OTS, Navigator OTS, Legend, Fascination, Emerald, Glory, Mariner OTS x 2, Sovereign OTS, Celebration, Miracle x 2, Pride, Fantasy
The group rate is a little more detailed than what is posted here. Yes you can get the group rate if you book 8 cabins but you must have at least 16 full fare patrons before you can get the free berth. Example 8 rooms booked but only 15 people going. No free berth. 8 rooms booked 17 people going but two rooms have 3 people to a room that means no free berth. The aminety points change based on the cruise. So be sure to check with Carnival to see what it is at the time you book.