13132HU.fa,13132HD.fa,13132Ltvec_small.FA 13132HU.fa,13132HD.fa,13132Ltvec_small.FA 13132HU.fa,13132HD.fa,13132Ltvec_small.FA 13132HU.fa,13132HD.fa,13132Ltvec_small.FA

I can't see how that's possible. The only thing you append to the file is a newline.

Here's a guess on what you're really looking for. You want to append the three files to the $fa file. You'll need to open each in turn, read from it, then print the contents to the $fa file (those variable names could really be more descriptive, by the way).

So I think what you want is something like this:

#!/usr/bin/perl
use strict;
use Data::Dumper;
use File::Glob ':glob';

my @dirs = glob("C:/Documents and Settings/mydir/Desktop/KOMP/*");

foreach my $maid_dir (@dirs) {
    # Combined the first two conditionals to reduce indentation
    if (-d $maid_dir and $maid_dir=~m%\d+\s[A-Z]%){ # match the dir na
+me
        my $seq_dir = $maid_dir."/sequencing/";
        chdir ($maid_dir) or die "Can't chdir to $maid_dir: $!\n";
        next if (-M $seq_dir > 1.0);
        chdir ($seq_dir) or die "Can't chdir to $seq_dir: $!\n";
        #print Dumper ($maid_dir, $seq_dir);
        opendir my $dh, "$seq_dir" or die "Can't open $seq_dir: $!\n";
        if(-d $seq_dir){
            my @files = readdir $dh;
            #my $path = @_;
            for my $f(@files){
                if($f=~ m%^(\d*)(HU.fa|HD.fa|Ltvec_small.FA|_fasta)$%)
+{
                    my ($fa, $hu, $hd, $lt)= ($1."_fasta", $1."HU.fa",
+ $1."HD.fa", $1."Ltvec_small.FA");
                    if(-e $fa){
                        # This is output, not input. Renamed variable 
+accordingly.
                        open( my $out, ">>".$seq_dir."/".$fa) or die "
+Can't open $seq_dir/$fa for append: $!\n";

                        # Append the contents of the three files to $f
+a
                        open my $hu_file, '<', $hu or die "Can't open 
+$hu: $!\n";
                        while (my $line = <$hu_file>) {
                            print $out $line;
                        }
                        open my $hd_file, '<', $hd or die "Can't open 
+$hd: $!\n";
                        while (my $line = <$hd_file>) {
                            print $out $line;
                        }
                        open my $lt_file, '<', $lt or die "Can't open 
+$lt: $!\n";
                        while (my $line = <$lt_file>) {
                            print $out $line;
                        }


                        #open( my $out, ">>".$seq_dir."/".$fa);
                        print $out, "\n" ;#"$hu,$hd,$lt\n";
                        print Dumper($f);
                        close($out);
                        close($hu_file);
                        close($hd_file);
                        close($lt_file);
                    }
                }
            }
        }
    }
}
[download]

Note that this is a very quick revision of your code, with added error checks (and just noticed I missed the readdir, doh). And it may not be at all what you want. If not, please provide more detail on what you're trying to do.

I want to append the three files to my $out file.
I only need each file appended once. The loop is appending each file
four times. Any ideas?

The -e checks for the existence of a file, not writability. So the file test in question won't guarantee that your file can be opened for appending.