I have a secured internet connection but never understood why, except to prevent people from piggybacking.
goofer, another reason to have a secured network (password protected wireless router) is that if your computer settings were set to share folders and files, and someone else wanted to break into your computer, they would have access to any shared folders and files and programs on your computer via the wireless network. I believe that the default in settings for Windows is set to not share, but if you ever wanted to connect your laptop to your desktop in your own home via the wireless router, you might have your settings set to share files. If someone else were to log on to your unsecured wireless network, at a house two doors down the street or from their car parked in the street, they could within a couple of clicks, see what other computers were on your network, and steal all of your shared files and programs within a couple of minutes.
Personally, I keep my two computers as separate computers, not networking them. My settings are set to not share anything. I like being able to jump on unsecured networks around town, and feel fairly safe doing so, but if someone didn't know what they were doing with their settings, their files might be vulnerable when they take their puter to the local Starbucks or other unsecured WiFi sites. When I used a wireless router at home, I kept it password protected.
Paula, I don't know what your liability would be if someone brought their computer. which was set up with shared files, to your rental cottage, then had their important information, like their company's employee records, stolen due to your wireless network being unsecured, but that type of liability is about the only reason I could think of on the downside of keeping it open access to all.