Judi Backer had an interesting post on the Facebook SW Rochester Community, Urban, and Permaculture Gardens group:  Build a $300 underground greenhouse for year-round gardening (Video)

This is something that would be well suited for for a year-round aquaponics system such as was discussed in the PLEX CAMPUS presentation http://youtu.be/SkHQxk-cOTw.  In that case they were thinking of using an existing cement wall building.  If starting with an empty back yard or lot however, it would make sense to dig down.  Green houses get expensive quickly if you're looking for something sightly to the non gardener. Keeping a low profile can let you put a large greenhouses in a backyard and have it almost unnoticeable from the street or from your neighbors back yards.  This link has a lot of good info also:  http://opensourceecology.org/wiki/greenhouses#Earth_Sheltered_and_W...