The most important thing is knowing that a router has two passwords: Admin and wireless network.
The admin password is what lets a person gain control of the router and change its settings. This can be accessed over wireless or wired ports. You do want to change the admin password.
The wireless network password is what you set when you enable wireless security. You should be using WPA, not the weak WEP, and the password must not be one that can be found in a dictionary. This password prevents people from joining the wireless network.
I won't go into more detail because there are many articles about this on the Web. I only wanted to point on the distinction between the router admin password and the wireless network password because many seem confused by it.