The best is to use the prepare method with placeholders:

my $sth = $dbh->prepare("INSERT INTO whatever VALUES(?, ?, ?, ?, ?, ?,
+ ?, ?, ?, ?, ?, ?, ?, ?)")

while (<INFILE>)   {
      my @line = (parse_csv ($_)); 
      $sth->execute(@line);
}
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This has the benefit of taking care of the quoting for you, but also of adding a performance increase, as just having to prepare the query once will save some time, as opposed to the DBI 'do' subroutine, which has to prepare it each time.