This should do it... I got surprised the $1 behaves differently if you loop through the array returned by /g matching, or if you stick the result of =~ in a while loop. Updated with various thoughts about this.

use warnings;
use strict;
use Data::Dumper; # for debugging

local $/ = ""; # input separator was newline, but now it's gone -> slu
+rp mode.
my $html;

while (<DATA>) {
    $html = $_;
}
print "Html: $html\n\n"; # just to check that this worked... it works.

#Don't do this, you can't use the $1, $2 type special variables.
my @matches = $html =~ m|(<B><P ALIGN=CENTER>(.+)</B></FONT>)|g; # use
+ | as regex delimitor to avoid leaning toothpick syndrome.
print "Dumper\n" . Dumper(\@matches); # bit o debugging

#Do this.  Then you can access the special vars.
while ($html =~ m|(<B><P ALIGN=CENTER>(.+)</B></FONT>)|g) {
    print "match $2\n"; # don't know why this works.  $1 doesn't work.
+  Hm...
}
#outputs
#match blah
#match foo
#match gah


#$line =~ m/<B><P ALIGN\=CENTER>(.+)<\/B><\/FONT>/gm;
#my $bit_i_want=$1;
__DATA__
<B><P ALIGN=CENTER>blah</B></FONT>
<B><P ALIGN=CENTER>foo</B></FONT>
<B><P ALIGN=CENTER>gah</B></FONT>
[download]

Maybe you should be using HTML::TokeParser to do html matching, regex matching on html doesn't scale too well.