People using my WiFi connection!

Why are people so afraid to connect to unsecured wireless networks? What can somebody see about me if I connect to their wifi connection? How do they see it?
I ask because I have a pretty powerful wireless router connected to cable broadband and I want to know who's connecting to it, if anyone. I also have reason to believe that my neighbor across the street is a pedophile.

You can sniff all packets on a wireless connection, it's highly recommended to encrypt them. Also, they can use your connections for illegal activities.
Use WPA/WPA2 to encrypt (WEP is not secure), also use MAC filtering on your wireless router, so only your devices can connect (actually this can be spoofed too, but it prevents the normal, stupid user from connecting).

if the Party Van shows up and confiscates all your computer equipment because a drive-by masturbator in the Free Candy Van hopped on your insecure wireless AP, you sir are fucked.

>>1
FBI can see you downloading Captain Picard