Wireless internet security

I recently moved into a basement apartment and I have access to wireless internet. This is the first time I'm using wireless so I'm curious about some issues. For example, is there a way that the home owner can tap into what I'm doing online? For instance. If I'm doing online banking and entering my passwords or posting questions such as this one, are they able to view my actions? In other words, how secure is wireless when it comes to privacy?

My experience with wireless is...

Wireless internet security