Our $org is embarking on the first attempt at sharing code within $depts. There's no business demand for it (but hey, we're non-profit), but we suspect that we're all reinventing the wheel. Smaller $depts within the $org will benefit too - they'll start building their apps with stronger code and it will lessen the likelihood of seeing freaky CGI code in production.
It's all volunteer work, but with benefits to the current tasks at hand.
Our first guess is that we need some sort of "CPAN" in place for our modules. Each $dept will submit a single module at first. We'll see if anyone uses it, how generic it can be ($org::$dept or just $org::), etc. Then we'll announce it among the $staff and see what more should be done for it to be useful.