In the category of Gram-negative bacteria, is there any non-pathogenic species? Is such a list of non-pathogenic gram-negative bacteria's available? Can you give maximum 5 examples of such bacteria which has been proved to be non-pathogenic and is gram-negative?
As Canadianer already mentioned in the comments, the majority of bacteria (this includes gram-negative bacteria) are non-pathogenic.
I think a prime example is the human gut flora. You can find loads of bacterial species living in your gut without doing you any harm, if anything they are doing you a favour by breaking down food.
Here some examples of gram-negative genera:
Most species within those genera are non-pathogenic, however, there are exceptions.
There are more than 15,758 named bacterial species, and the majority of them are Gram-negative, and most of them are non-pathogenic.