UPDATE `table_name` 
SET `field_name` = (SELECT CASE `field_name` WHEN 1 THEN 0 ELSE 1 END) 
WHERE `id_column` = 1

Or with text strings

UPDATE `table_name` 
SET `field_name` = (SELECT CASE `field_name` WHEN 'foo' THEN 'bar' ELSE 'foo' END) 
WHERE `id_column` = 1