%hash = (
    key1 => 10,
    # ...
);

##</code><code>##

my %freq;
my ($max_freq, $max_value) = 0;
for my $value (values %hash) {
    $freq{$value}++;
    if ($freq{$value} > $max_freq) {
        $max_freq  = $freq{$value};
        $max_value = $value;
    }
}
print "$max_value: $max_freq times\n";