DO memorize your password. Passwords are case-sensitive. DO choose a completely new password every time you change. Once they get your password, they can do awful things to any information stored in your account. Even worse, they may be able to do awful things to the accounts of other people on the system, or even break in to systems across the world from ours.
System security is everyone's responsibility.
Because you don't know where the information will go after it leaves your lips. Even if you only tell one other person, they could tell one other person, and so on, until your password is in the hands of an Evil Cracker. On most UNIX systems you're not supposed to share your account with someone else. So there would be no legitimate reason for them to use your password. Again, because you don't know where the information will go after it leaves your brain.