Almost all public Wi-Fi's I have encountered require you to press a button on a webpage (or even make an account), before you can use it. But one time it was just "To use our Wi-Fi, just press the button below!". Not only is it inconvenient for the user, but it also destroys innovations like auto-connect. It even makes it very difficult or even impossible to connect with some devices, like the Nintendo DS. Why are they doing this?
Usually it's a Terms of Service agreement, and by clicking the button you're agreeing to the terms. I never read them but they probably have the usual disclaimers, no guarantee of privacy, etc.
The problem as stated is that many public wifi locations need to provide a ToS and force you to agree to it to use the wifi. This is problematic for devices that don't use browsers. There are some solutions but most of them aren't acceptable:
Put a sign up when entering the premises. People don't read signs and even if they do they can claim they didn't
Leave the network wide open. This causes all sorts of liability issues in several arenas. Some of these issues can get very costly
Provide a secure login that can be remembered by the device.
I prefer the 3rd option. It takes a little more effort from the user, but once the account is created and remembered by the device all future uses of the wifi avoid the button clicking site. It can also allow non-browser using devices to connect through normal wifi connection methods. It also requires the user to take steps to release the location of liability. Again it requires a bit up front, but in the end is a win-win for all those involved.