a situation where I would want my program to duplicate itself in memory and start doing the exact same thing twice ... I don't see why it's necessary or useful

The point of fork is not really for the parent and child to do the exact same thing. If you look at its documentation, you'll see that the parent and child get different return values, allowing them to follow different code paths. Typically, the parent will fork multiple children and then manage them, while the children will be doing various tasks. This scheme is widely used in many web servers, see e.g. preforking server. For just two examples of many in Perl, see Parallel::ForkManager and Net::Server.

For example, certain calculations could profit from it if one distributes them on several CPUs. What else do you have the expensive gizmos for? Here is a simple, admittedly somewhat pointless example:

#!/usr/bin/env perl

use strict;
use warnings;
use Math::BigInt;
use Parallel::ForkManager;
use Time::HiRes qw ( time );
use feature qw(say);

my $sleep_period = shift;
my $processes = qx(sysctl -n hw.ncpu);

chomp $processes;

my $pm = Parallel::ForkManager->new($processes);

$pm->set_waitpid_blocking_sleep($sleep_period);

say qq(processes: $processes);

my $start = time;

for my $number ( 1 .. 50 ) {
    $pm->start($number) and next;
    my $factorial = Math::BigInt->bfac(2000) for 1 ... 10;
    $pm->finish(0);
}
$pm->wait_all_children;

say qq(fork: ), time - $start;
[download]

See also this eight-year-old thread from which the example comes.