That depends on a number of things.
Was the password for the wireless access or for accessing the router settings? Almost every router comes with a default password on the router settings page, it's often something basic like "password". You don't really need to change that password because once your wireless password is turned on, nobody should be able to access the settings page anyway.
Secondly, if it is the wireless access password you're talking about then it is best to change it from the default immediately, the password might not be unique and anyone trying to access your network would just need to Google your router model (which is often displayed by searching for nearby networks) to find out what the password is. Creating your own unique password is the best option here to secure the network.
Thirdly, the wireless access password should be set to WPA2 encryption. WEP is easily hackable, WPA is a more secure version of WEP that was rushed out when WEP was found to be faulty, and WPA2 is the current wireless encryption standard which offers a good level of security.
(If you don't secure the network, not only might people be able to access files on your computers, they could even alter the network's settings to deny you access. I've heard of this happening a few times, some people actually drive around looking for unsecured networks just to piss people off like that.)