Galaxy class was a term used to describe at least two different types of starship. In the 26th century, Draconian battle cruisers were described as "Galaxy class". (TV: Frontier in Space)
"Galaxy class" was also a rating for passenger starships. Large and luxurious, capable of carrying four thousand crew and passengers, they could go for years between planet fall and typically could produce their own air. They were in use in the 44th and 51st centuries. (TV: Flesh and Stone, A Christmas Carol)
One starliner on which Amy Pond and Rory Williams honeymooned in the 44th century almost crashed into the planet Ember until the Eleventh Doctor and Kazran Sardick had Abigail Pettigrew sing the skies calm. (TV: A Christmas Carol)
The Byzantium was a Galaxy class starship that Weeping Angels crashed on Alfava Metraxis in the 51st century. (TV: The Time of Angels)
Another ship of this class, similar to the Byzantium, arrived above Trenzalore, along with many other ships in response to the signal emanating from the planet. (TV: The Time of the Doctor)
The designation was given to one of several versions of the starship USS Enterprise in a parallel universe. (COMIC: Assimiliation²)