Quick definition of terms for my response:
OPEN = Open all the way to the Internet - no passcode
Unsecured = No authentication to connect, but must "agree to terms" before a connection to the Internet - no passcode
As long as you don't connect to an OPEN or Unsecured network you should be fine. What you have to watch out for is, if you have connected to an OPEN network in the past by the name (SSID) of, say, Linksys or Netgear for example, (or other common name) when you accidentally get near another OPEN network named Linksys or Netgear your phone will automatically connect. So, regarding security, it is best to keep Wifi turned off until you are ready to use it and can control what network you connect to.
As far as an Unsecured network goes, since you have to check a box to agree to the terms and click on [OK] (or similar), you won't auto-connect to the Internet in places like Starbucks and McDonald's. Even though the internal network uses the same name in all the locations (I think Starbucks and McDonald's is "attwifi", or similar). But... the risk of the internal network is also very important. You don't want other people in neighboring seats "browsing" your phone or laptop. So still, regarding security, keep Wifi off until you're ready to use it. Kinda like a gun
I have to add though, security should be in balance with functionality verses risk. Only you can decide what is best for you. One persons paranoia is another person's necessity. Just depends.
-Frank