use Cwd;

$homedir = getcwd();
@dir = $homedir;

$feddir = "";
@allfiles = ();
@dirnw = ();
@directory = ();
@files = ();

sub putdir {
        $directories = "";
        $spacefiles = "";
        opendir (THISDIR, "$feddir") or die "dying! $feddir: $!";
        @allfiles = readdir THISDIR;
        closedir THISDIR;
        foreach $a (@allfiles) {
                chomp $a;
                if ( $a eq "." || $a eq ".." ) {
                        next;
                        }
                elsif ( -d $a ) {
                        if ($directories eq "") {
                                $directories = "$a";
                                }
                        else {
                                $directories = "$directories+" . "$a";
                                }
                        }
                else {
                        #it should detect if the file has a space in i
+t first
                        $rest = "";
                        (undef,$rest)=split(/\s+/,$a,2);
                        if ($rest ne "") {
                                if ($spacefiles eq "") {
                                        $spacefiles = "$feddir/$a";
                                        }
                                else {
                                        $spacefiles = "$spacefiles+" .
+ "$feddir/$a";
                                        }
                                }
                        }
                }
        $rtrn = "$directories%" . "$spacefiles";
        return $rtrn;
        }

do {
        foreach $feddir (@dir) {
                chomp $feddir;
                $output = putdir();
                ($dirs,$file) = split(/\%/,$output);
                (@files) = split(/\+/,$file);
                open (DATABASE, ">>/$homedir/listofiles");
                        foreach $f (@files) {
                                chomp $f;
                                print (DATABASE "$f\n");
                                #$g = $f;
                                #$g =~ s/\s+/_/g;
                                #rename $f, $g or die "can't rename! $
+f, $g: $!";
                                #$g = "";
                        }
                close DATABASE;
                (@directory) = split(/\+/,$dirs);
                foreach $d (@directory) {
                        chomp $d;
                        (undef,$restodir)=split(/\s+/,$d);
                        if ($restodir ne "") {
                                open (DATABASE2, ">>/$homedir/listodir
+s");
                                print (DATABASE2 "$d\n");
                                close DATABASE2;
                                #$h = $d;
                                #$h =~ s/\s+/_/g;
                                #rename $d, $h or die "can't rename! $
+d, $h: $!";
                                #$h = "";
                                }
                        }
                push @dirnw, @directory;
                @directory = ();
        }
        @dir = ();
        @dir = @dirnw;
        @dirnw = ();
} until (@dir == "")
[download]

I'm not sure why you're doing a few things there:
• taking a list and returning it spliced together as a string, only to split it again (why not return two array refs instead?)
• doing a split just to find out if there's a space character in a filename (why not just use m// ?)
• chomping filenames from readdir (where would the newlines have come from?)
• using @dir == "" rather than just @dir to detect whether an array is empty
• what does the code do when you have a file or directory name with a '+' or '%' character in it?
• re-opening your database for each file/directory

What's wrong with something like:

use File::Find;
use Cwd;
my $homedir = getcwd();

open DATABASE,  ">>$homedir/listofiles" or die "can't open listofiles:
+ $!\n";
open DATABASE2, ">>$homedir/listodirs" or die "can't open listodirs: $
+!\n";

File::Find::find( sub {
  return if /^\.\.?$/;
  return unless /\s/;
  if ( -d $_ ) { print DATABASE2 "$File::Find::name\n"; }
  else { print DATABASE "$File::Find::name\n"; }
  ( my $newName = $File::Find::name ) =~ s/\s+/_/g;
  print STDERR "renaming $File::Find::name to $newName\n";
  # rename($File::Find::name, $newName) or die "can't rename : $!\n";
 },
 $homedir
);

close DATABASE;
close DATABASE2;
[download]