Of course, it's easier to watch the screen than fingers. Most systems have the sophistication to not display passwords as they are being typed.
A more high-tech method of eavesdropping is to place a wiretap on the communications line and watch all the passwords (and everything else, for that matter) go by. Whether this is easy or hard depends on the environment. There are also software-based keystroke logs that can be covertly installed on PCs and even hardware logging devices that can be embedded in keyboards or cables.
If you're going to give up on memorization and accept the risks of written-down passwords, an effective mechanism is one-time passwords. Here, the user and the system have a list of valid passwords, but each one is only valid once. After it's used, it is crossed off the list (at both ends). Periodically, the user must get a new list from the system administrator. This mechanism is nearly impervious to eavesdropping.
A variant is to have a numbered list of passwords and have the system ask for specific ones on each authentication. An attacker would have to eavesdrop on many authentications before obtaining enough information to impersonate the user. With this technique, the list can be somewhat shorter and can be used for longer than the one-time password list, but at some loss of security and convenience. (See Homework Problem 2.)