Suppose I have a wireless router and computer with Wireless card connected to it.Can a second computer intercept the data exchange between the router and first computer? And can this cause a security problem - eg. if the first computer transmits username/passwords of bank account ? How to protect against this threat ?

be sure to have either wep or wpa encryption turned on, and you can also encrypt the info being sent from pc to pc.

Your wireless signal can certainly be hijacked. Mine was, and I just got off the phone with the router manufacturer (Linksys), after a lengthy conversation on how to reset my wireless. My signal had been hjacked for days until I got the answers from Linksys. Call your router manufacturer, or look it up in a Google search. They will be able to help you set a password and a way to prevent hijacking. Get the phone, sit down at the computer and call them. Wireless hijacking is a growing problem for all the wireless users. Prevent this by stopping it before it starts.