#!/usr/bin/perl

while ( <DATA> ) {
   print if /<b>/ .. /<br>/;
}

__DATA__
a whole
lot of  worthless
stuff
<b>Title:
</b>
STRING_I_WANT<br>
more worthless
meaningless stuff
or sometimes
<b>Title:
</b>ANOTHER STRING_I_WANT<br>

##</code><code>##

/users/rc6286 > perl test.perl
<b>Title:
</b>
STRING_I_WANT<br>
<b>Title:
</b>ANOTHER STRING_I_WANT<br>