So I don't know anything about this stuff but looking at the XKCD example it looks really easy to see virtually everything my neighbours are doing on the web. What am I missing? Or is it really this insecure to use wireless?
Encryption. Your neighbours hopefully have protected their wifi with a password. This prevents casual snooping but of course can't really keep out a dedicated attacker. There are automated tools to break WPA encryption.
Additionally, if your neighbours are browsing using SSL/TLS then you theoretically cannot eavesdrop on those sessions.
If you are able to get the key or they use no encryption or WEP you can look at the packets and get metadata for SSL sessions and all unencrypted traffic.
And that includes source/destination IP? Didn't know that..
If you can hear the signal, you can capture the traffic.