The importance of grammar in language

I know that google translate is not based on any grammatical analysis but on the statistical analysis of a language database, but we are human beings and sometimes enjoy processing natural languages in grammatical terms. We are all linguists in a sense.

I suppose nobody can deny the importance of grammar in language, and we should differentiate between rules that we can describe in simple grammatical terms and those that we really follow but cannot describe clearly. The discussion should be focused on how important, or useless, specific grammar terms and rules are on which level of learning.