I'm the VP of the Linux users group at the University of Delaware and we have several servers in the central data center connected to the university's subnet(128.4.0.0/16) with unfettered access to the general internet. No NAT, and limited firewall.

Our Webserver is on a subdomain of the .edu(lug.udel.edu) and is totally accessible from the internet. It even listens for incoming connections. We run a mail server, a mirror, and an IRC server on there. It's great because even alumni can connect from wherever. I think there is a central firewall for every connection coming in, but I haven't run into problems for my uses.

In fact, every system registered for an IP on the UD intranet is assigned a public, world-accessible IP on the 128.4.0.0/16 subnet and can listen for incoming connections. Even wireless devices.