I don't get why people change their router's password. No one else will be able to change the settings without being connected to it.
You do realize that others can connect to your router remotely right? There is all the reason in the world to put a password on your router.
It is inherently impossible to fully secure a network from threats, but putting up at least a little resistance prevents those casual threats (like your next door neighbor's kid pretending to be a hacker).
Ideally your router should have a new password, MAC address filtering should be in place, if it's a wireless router you should turn off SSID broadcasting and enable WPA 128-bit encryption.