For the record, having a simple password with a pattern is a bad idea in the long run - It is far too easy for people to spread it around, guess, etc.
When are simple passwords ok?
Some people say never, but in the interests of convenience, and to smooth transitions in service updates, simple passwords used for a limited time period can be an acceptable risk. For example, during administrative work, all users may be reset to a pre-determined password or pattern of passwords; however, the user should be forced or expected to change their password as soon as possible (i.e. immediately upon notification).
On many servers (for example, Hosted Terminal Services), there are password complexity tools we can use on the server to enforce a minimum level of security. These tools can be annoying to some people, but what you have to keep in mind here is that your information is theoretically accessible to remote users.
Many companies will have specific IT policy detailing password complexity requirements as well. If you are dealing with your own information and want a simple password, that is your choice; however, when you are dealing with your employers information, or information of clients, you have to consider their requirements and best interest.
There's no law against using your drivers license number or birth year as your bank pin, but most people would agree it's a bad idea.
Staff Turnover
A key concern for many organizations relating to passwords and information security is staff turnover. If staff are changing, passwords should change. Ideally at the same time. In any environment, it's possible for people to share (intentionally or accidentally) login information with other staff. When a staff member leaves, all other staff should immediately change passwords. Doing so is good for the security of the companies data, and it's also good for the ex-staffer as well. Consider an event where data goes missing immediately following the departure of an employee. Without password changes there is a possibility that either the data loss was intentional (though I'm sure we all hope anyone leaving an organization does so on good terms, there are times it doesn't happen), or it could be accidental and coincidental - without a password change, the question may never be answered.
In our role as system administrators, a client may call to tell us:
"Someone is changing roles this Friday at 2pm" - and then on Friday we get a call "Please disable bob's access immediately, close any open logins, and force all users to change passwords on next login".
Sharing Passwords
This is NEVER a good idea. Though sometimes where the password in question has limited risk it is commonly done, please remember that giving someone your password is the equivalent of giving them the opportunity to impersonate you. Our staff will never ask for your password, though we may have to request you to log into a system, or we may have to reset your password to accomplish certain tasks.
All passwords are stored using encryption intended to prevent anyone (including administrators) from seeing the original password.
Emailing Passwords
In general, DON'T. Email often passes unencrypted through MANY networks and computers - each of which provides an opportunity for interception. Even if you are sending to someone in your own company, unless you are sure your mail system uses encrypted transport, you should not proceed. If you must, please change the password as soon as possible thereafter.
One Time Passwords
Some advanced procedures like BlackBerry Enterprise Server activation will require single use or one time passwords. These passwords are used to confirm or complete an action, and are invalid as soon as they are complete. Sometimes these passwords are made shorter and less complex than normal, particularly when the user may have difficulty entering them (unusual keyboards, etc. with mobile devices are a common reason), however, note that because these passwords can not be reused their simplicity does not add any significant risk.