I can access a university's WLAN with my desktop, which is about two miles away. First, what kind of wireless router are they using, and, am I stealing Internet access? Should I tell them about this? I can also do this with my neighbor's network.
You are stealing access, at least from your neighbor. The university probably has the access point set up for students who pay a fee, and in that case, you are stealing access from them as well. Even the open hot-spots generally charge some fee for access to those they allow to use them. If they leave them open as a service (like in some hotels), it is generally intended for guests. There is a practice in this country called war chalking where people go around and snoop for open antennas and then place a chalk X on the sidewalk to let others know where they can access the net. It's kind of like anything else on earth, nothing is really free. I would suggest calling the university and letting them know that it is open. This is a huge cause of identity theft in this country. Some people even set up open access points just so they can snoop what is going on and get information. If they let you use it, then fine, if not, you could get in trouble. I would also suggest that you tell your neighbor that his is open as well.
As for the distance of two miles, and what type of router they are using – who knows! You could be attaching to a university professor that lives in your neighborhood or someone else with a university access point connected via cable modem or DSL, so just knowing that it says the university's name is no guaranty that it is physically located at the university.