if condition in sql server update query

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.

Something like this should work:

UPDATE
    table_Name
SET 
  column_A = CASE WHEN @flag = '1' THEN column_A + @new_value ELSE column_A END,
  column_B = CASE WHEN @flag = '0' THEN column_B + @new_value ELSE column_B END
WHERE
    ID = @ID