For access to router / switch using Telnet we use the Virtual Teletype (VTY) lines. To protect VTY port from unwanted access, we must configure password on this port. Also, if password is not configured and enabled, Telnet access will not be possible.
Router#config t
Router(config)#line vty 0 4
Router(config-line)#login
Router(config-line)#password newpassword
With password newpassword we can set new password for vty port, and with login we activate it. Also, we can use no password to delete password, or no login to disable it.
If you try this
Router(config)#line vty 0 ?
<0-4> Last Line Number
<cr>
Router(config)#
you will see that you have 5 VTY lines, and it is possible to configure different password for each. You can not choose on which line you will be connected using Telnet, so different passwords can cause troubles.
To enable access without password, try this
Router(config)#line vty 0 4
Router(config-line)#no login
Do not forget always to save new settings.