It's a very simple solution.
If you can see the router, you may actually be able to administrate it. The default address is 192.168.1.1 or 192.168.0.1 on these routers. You can find the default password for it on the net. Usually something like "linksys" or "password".
If you can administrate it, you can set a few passwords up on behalf of the owner. Like, "IWILLNOTLEAVEMYROUTEROPEN"
> Someone could get your sensitive info very easy, like banking.
Actually, that's not true. That's not the problem. The problem is that a person who is using it could be using the internet connection to download really illegal things, like Child Pornography. It's very difficult to sniff HTTPS traffic.
Now the other issue is that if you have unsecured machines on your network and the gateway is bridging traffic to your LAN, you can face a situation where the person connecting to your wireless gateway can also see the entire contents of your hard drive and any other device. (In theory, being able to print to a network printer.)
There have been cases where the cops have busted down the door of people who had an open wireless gateway because it showed that child pornography was being downloaded from their IP address. It turns out that a really perverted neighbor was downloading it instead because they didn't secure their wireless gateway.
So, while it's great to share your internet connection, no good deed goes unpunished!