There in fact are method(s) that limit the number of results you get. They're called fetchrow_*(). They limit the number of results to one row so you can control however many you actually obtain. Straight out of the DBI documentation:

$sth = $dbh->prepare("SELECT foo, bar FROM table WHERE baz=?");

$sth->execute( $baz );

while ( @row = $sth->fetchrow_array ) {
    print "@row\n";
}
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Now you can transform this a little to suit your needs like merlyn was talking about:

my $LIMIT = 30;

my $sth = $dbh->prepare("SELECT foo, bar FROM table WHERE baz=?");
$sth->execute( $baz );

my ( @rows, @row );
for ( 1 .. $LIMIT ) {
    last unless ( @row = $sth->fetchrow_array );
    push @rows, [ @row ];
}

#do stuff with @rows
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This code is untested but you get the general idea. There are other types of fetchrow_*() methods that you can take a look at. Read the DBI documentation.

Update: You can also take a look at the fetchall_arrayref() method which appears to take a $max_rows parameter.