Index of the row with most non-zero elements
MATL, 6 bytes

!gs&amp;X&gt;


Input is a matrix, with ; as row separator.

Try it online! Or verify all test cases.

Explanation

!     % Transpose
g     % Logical: convert non-zeros to 1
s     % Sum of each column, or sum of row if there's a single row
&amp;X&gt;   % Arg max. Implicitly display