Pass SSH password automatically

[Steve Searle]

Many moons ago I set up my (then RH) Linux box to pass the current
password automatically when SSHing to another box.  If I was logged on
as steve, and I did "ssh myserver" it would take me straight to a shell
on myserver, logged on as steve, assuming the steve account on myserver
had the same password as the box I was coming from.  I was not asked for
the password.

Does anyone know what I need to change to change my current setup to
work like this.

Cheers

Steve