Mail::Address maybe, probably. :P

use Mail::Address;
my $raw = 'My Name <email@example.com>';
my @addresses = Mail::Address->parse($raw);
print $_->address, $/ for @addresses;
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Update: posted before I saw haukex's answer. I am not sure which of Mail::Address and Email::Address is a better choice or if they are equivalent. The former was already installed on my box. :P