my $line;
while ( <DATA> ) {
   chomp;
   $line = $_;
   $line =~ /\s+<\w+\/?>(.*)<\/\w+>/;
   $line = $1;
   print "$line\n";
}
[download]

In addition to the other comments you got, you should as usual declare your lexical variables in the innermost scope as possible; in this case:

while ( <DATA> ) {
   chomp;
   my $line = $_;
   # ...
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But... all in all it's strange that you use the implicit $_ only to assign it to $line. You either want

while ( <DATA> ) {
   chomp;
   /\s+<\w+\/?>(.*)<\/\w+>/ or next;
   print $1, "\n";
}
[download]

or

while ( my $line=<DATA> ) {
   chomp $line;
   $line =~ /\s+<\w+\/?>(.*)<\/\w+>/ or next;
   print $1, "\n";
}
[download]