No longer have to enter a password to SSH into another server?

Solution 1:

Check out this article. Essentially, I believe you're looking to generate and share keys between the local and remote machines in each ~/.ssh folder. The article outlines it better than I could. (And if that fails you, it's an easily Google-able subject).

Solution 2:

ssh keys + an ssh-agent, you may also want to look into keychain. Read the following set of gentoo articles by Daniel Robbins for a good overview on openssh key management.

Solution 3:

Most likely host-based authentication is enabled.

Look for the section on host-based authentication in the ssh manpage, and look for RhostsRSAAuthentication or HostbasedAuthentication in /etc/ssh/sshd_config