Avoid use of risky applications. In the UNIX world, don't use rlogin, rexec, rsh and other remote commands that don't require authentication. Whenever possible use a direct dial-in or an encrypted application that is immune to snooping and spoofing. Anytime you use X, you should be using the security features that your X terminal provides. Without explicitly using X security, anyone on the Internet could in theory create a connection to your X terminal and monitor everything displayed on your X terminal.
X security comes in two flavors, key based and host-based.
If you start your X session by logging in through an on-screen login dialog box, a random key is assigned to you and saved in your home directory. Any X programs you start can read the key from a file and provide it to the X terminal to establish proper authority to access the X terminal. This is the highest level of X security available, and should always be used. It is not available, however, on Mac X, and does require logging in through the XDM on-screen login system. Logging in with XDM does not automatically turn off host-based security privileges on all X terminals, though.