Another way to do it:

use strict;
use warnings;

my %data;
[download]

map {chomp $_->[2]; $data{$_->[0]}{$_->[1]}{$_->[2]} = ''} [split /\s+
+/]
    for <DATA>;
[download]

$data{$_->[0]}{$_->[1]}{$_->[2]} = '' for map [split], <DATA>;

for my $num (reverse sort keys %data) {
    print "$num\t$_\t", (join ",", keys %{$data{$num}{$_}}), "\n"
        for keys %{$data{$num}};
}

__DATA__
848    05/23/06    11:00
848    05/23/06    12:30
848    05/23/06    13:00
848    05/23/06    14:00
848    05/25/06    11:00
848    05/25/06    12:00
261    05/24/06    11:00
261    05/24/06    12:30
261    05/24/06    13:00
261    05/24/06    13:00
261    05/24/06    13:00
261    05/24/06    13:00
[download]

Prints:

848    05/23/06    12:30,11:00,14:00,13:00
848    05/25/06    11:00,12:00
261    05/24/06    12:30,11:00,13:00
[download]

Update: apply jwkrahn's neat round of golf