I agree about the foreach loop.

In addition, the actual error message (apparently) refers to the variable $IP as being undefined; this is because the assignment to $IP is using a different hash than the one that is being looped through. The loop starts with:

foreach $key(%Servers){
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which loops through all of the key/value pairs of the hash %Servers in pseudo-random order (probably not what you wanted, as runrig has said). However, your assignment to $IP uses the variable $key to retrieve values from another hash called %Server, which is undoubtably empty, in fact making $IP undefined.

Also, as has been noted elsewhere, you most certainly do not need the double quotes around scalar values, for example, $Server{$key}: they force unnecessary interpolation, since $Server{$key} itself is already a string.

There is no particular reason to use a hash at all, preferring an array, which will preserve your ordering of IP addresses. I would go one step further and remove the unnecessary call to chomp (since the addresses do not end in newlines):

my @Servers = qw( 128.37.37.201
                  128.38.38.201
                  128.39.39.201 );

foreach my $IP ( @Servers ) {
  my $FTP = Net::FTP->new($IP);
  if ( $FTP->login($user,$pass) ) {
    $FTP->ascii();
    $FTP->put($File);
    $FTP->quit;
  }
  else {
    print "Error logging in to $IP: ". $FTP->message ."\n";
  }
}
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dmm

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