Your Perl code looks functional, so aside from using other packages, I would only critique the style and some minor points.

1. http://www.cc2e.com/Default.aspx 'Code Complete' is an excellent style guide for any language
2. http://www.oreilly.com/catalog/perlbp/ 'Perl Best Practices' is another book specifically for Perl

#!/usr/bin/env perl
#    I'm just assuming the above line works...?

# This program presents a list of hard-coded hostnames to the user and
+ lets them ssh to one by choosing it's number
# ^^ give love to da maintenance programmer

use strict; # Good!!
use warnings; # Better!!

# It's good practice to identify your globals by making them upper-cas
+e
our $USER = 'brannont';
our @HOSTS = qw(
          secdevfdsapp01
          dopey
          bonnie
         ) ;

# Use full path of program for exec to avoid security issues
our $SSH_PROGRAM = '/usr/bin/ssh';

# Moved the main program execution up here so the maintenance programm
+er doesn't have to read the whole program to see what it does...

our $SSH_ARGS = &get_ssh_args();
print $SSH_ARGS, "\n" ;

exec $SSH_PROGRAM, $SSH_ARGS;

# Gets the selected hostname from the user and returns
# the arguments we'll need to pass to the 'ssh' command
sub get_ssh_args {
  my $chosen_hostname = &choose_host();
  return &ssh_string($chosen_hostname) ;
}

# For a given host, return the ssh arguments to allow us to
# login as a hard-coded user on that host
sub ssh_string {
  my $host = shift;
  # Suggest also appending your domain here:
  return &username() . "@" . $host . &domain();
  # 'Programming Perl' suggests avoiding use of printf()
  # sprintf "%s@%s", $user, $host
}

# Prints the list of hosts with numbers in front to allow
# user to make a selection
sub printchoices {
  print "\n\n",
        "ssh hosts\n",
        "---------\n";
  for (my $i=0; $i < &num_hosts(); ++$i) {
    print "[$i] ", &hostname_by_num($i), "\n" ;
  }
}

# prints a prompt for user input
sub prompt {
  return "\n\nssh to: " ;
}

# Gets the user's chosen host
sub getchoice {
  print &prompt();
  my $choice = <STDIN> ;
  chomp $choice;
  return $choice;
}

# Get the user's chosen host (by number) or die trying
# renamed from 'mainloop'
sub choose_host {
  my $chosen_host;
  while ( !$chosen_host ) {
    &printchoices();
    my $user_choice = &getchoice();
    if( ($user_choice =~ /^\d+$/) && 
        ($user_choice >= 0) && 
        ($user_choice < &num_hosts()) ) {
      $chosen_host = $user_choice;
    }
  }
  # May as well dereference the name here...
  return &hostname_by_num($chosen_host);
}

# These three functions are simple lookups to the globals 
# now, but in the future they can be expanded
sub num_hosts { return scalar(@HOSTS); }
sub hostname_by_num { return $HOSTS[ $_[0] ]; }
sub username { return $USER; }

# In the future, this could return our domain
# eg. ".example.com", possibly from a global
sub domain { return ""; }
[download]

The program could be made a lot simpler by combining functions, etc..., but thats not necessarily an advantage from the long term maintenance perspective.

On the other hand, the program was so simple that it's not going to be much of a headache to maintain in the future as-is. The changes I suggested are what I'd suggest to a novice Perl programmer who turned in the above code for deployment on a production system.