Danfoss do a series of DC refrigeration compressors. It might be possible to replace the compressor in your existing fridge or freezer.
See here....
http://www.rparts.com/Catalog/Major_Components/compressors/Danfoss/danfoss.aspMost of the 12v compressor fridges, like the Sundance ones, use these.
12v microwaves are readily available but cost the earth. I'd be tempted to run a 240v one off an inverter. Many other 12v devices seem to be under powered. I know the 12v kettles take an eternity to boil, the toasters seem to dry the bread before toasting it! I've no experience of them but I reckon the 12v slow cooker would work well. Satellite receivers, freeview boxes, DVD players and smaller LCD TV's are all available in 12v and probably work as well as any mains device. HTH.