I have a SQL server table in which there are 2 columns that I want to update either of their values according to a flag sent to the stored procedure along with the new value, so
The current answers are fine and should work ok, but what's wrong with the more simple, more obvious, and more maintainable:
IF @flag = 1
UPDATE table_name SET column_A = column_A + @new_value WHERE ID = @ID;
ELSE
UPDATE table_name SET column_B = column_B + @new_value WHERE ID = @ID;
This is much easier to read albeit this is a very simple query.
Here's a working example courtesy of @snyder: SqlFiddle.