use strict;
use warnings;

local $/ = "<br>";
while ( <DATA> ) {
   print $1 if /Title:(.*?)<br>/s;
}

__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>
[download]

update: This should take care of the extra stuff. I reread your requirement, everything from "Title:" to <br> and did what that specified instead of just the strings you wanted. The following only retrieves those strings and shows you how to put it in a variable (basically assign $1 to something) (see rob au's response which answers the question you asked). Good luck, here is the code:

use strict;
use warnings;

local $/ = "<br>";

while ( my $line =~ <DATA> ) {
   if ( $line =~ /Title:.*?<\/b>\n?(.*?)<br>/s ){
    my $saved_var = $1;
    print "$saved_var\n"
   }
}

__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>
[download]

-enlil