First, I added use strict and made a couple changes to make that work. I also removed the pointless return 0;.

Next, I removed the chdir and changed the recursion line to:

MakeDirs("$base/$dir_name", $num_dirs, $depth - 1);
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Finally, I removed the mkdir loop, and added mkdir $base; near the top of the program. This makes every recursion make one directory, which is how I like my recursion to work. It also has the added advantage of creating the initial directory if it doesn't exist.

My finished code follows:

#!/usr/bin/perl

use strict;
use warnings;

sub MakeDirs($$$);

MakeDirs("/hpq", 2, 3);

sub MakeDirs($$$)
{
    my($base, $num_dirs, $depth) = @_;
    
    mkdir $base;

    #if depth = 0, no more subdirectories need to be created
    if($depth == 0)
    {
        return 0;
    }

    #Recurse through the directories
    my $dir_name = "a";
    for(my $x = 0; $x < $num_dirs; $x++)
    {
        MakeDirs("$base/$dir_name", $num_dirs, $depth - 1);
        $dir_name++;
    }
}
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