# assume you have a $toppath, which is where the traversal starts

chdir $toppath or die "can't cd to $toppath: $!";

open( FIND, "find . -type d -print0 |" ) or die "can't run find: $!";

# find will traverse downward from current directory
# (ie. $toppath), and because of the "-type d" option,
# will only list the paths of directories contained here;
# the "-print0" (thanks, etcshadow) sets a null byte as the
# string terminator for each file name (don't rely on "\n",
# which could be part of a file name).

{
  local $/ = "\x0";  # added thanks to etcshadow's reply
  while ( my $dir = <FIND> ) {
    chomp $dir;
    unless ( opendir( DIR, $dir )) {
        warn "$toppath/$dir: opendir failed: $!\n";
        next;
    }
    while ( my $file = readdir( DIR )) {
        next if ( -d "$dir/$file" ); # outer while loop will handle all dirs
        # do what needs to be done with data files
    }
    closedir DIR;
    # anything else we need to do regarding this directory
  }
}
close FIND;