my $url = "http://www.nukeforums.com/forums/viewforum.php?f=17";
my $ua = LWP::RobotUA->new;
my $lp = HTML::LinkExtor->new(\&wanted_links);

my @links;
get_threads($url);

foreach my $page (@links) {
    ...
}
[download]

my $ua = LWP::RobotUA->new;
my $lp = HTML::LinkExtor->new(\&wanted_links);

my @links;

foreach my $forum_id (17, 3) {
    my $url = "http://www.nukeforums.com/forums/viewforum.php?f=$forum
+_id";
    @links = ();  # yuck!
    my $links = get_threads($url);
    foreach my $page (@$links) {
        ...
    }
}
[download]

As you can see, I don't like your use of the global variable @links. We're forced to provide and initialize a variable that should be local to get_threads. Here's the fix:

#!/usr/bin/perl
use strict;
use warnings;

use LWP::RobotUA;
use HTML::LinkExtor;
use HTML::TokeParser;
use URI::URL;

use Data::Dumper; # for show and troubleshooting

my $ua = LWP::RobotUA->new();

foreach my $forum_id (17, 3) {
    my $url = "http://www.nukeforums.com/forums/viewforum.php?f=$forum
+_id";
    my $links = get_threads($url);
    foreach my $page (@$links) {
        ...
    }
}

sub get_thread {
    ...
}

sub get_threads {
    my $page = shift;

    my @links;
    my $lp = HTML::LinkExtor->new(sub {
        my($tag, %attr) = @_;
        return unless exists $attr{'href'};
        return if $attr{'href'} !~ /^viewtopic\.php\?t=/;
        push @links, values %attr;
    });

    my $request = HTTP::Request->new(GET => $url);
    my $response = $ua->request($request, sub {$lp->parse($_[0])});

    # Expand URLs to absolute ones
    my $base = $response->base;
    return [ map { url($_, $base)->abs } @links ];
}
[download]

Update: Added the minimal change.

Edited by planetscape - Reparented from Reaped: LWP & HTML::LinkExtor running recursively against a bulletin board to Re^3: proof of concept how to run this code