Unfortunately, the nature of computer and Internet security is such that you can't do that. Different networks, sites and applications have their own password requirements and more classified or personal information merits stronger, more unique authentication.
It is difficult when your employer requires a password of at least 8 characters that must include at least one number and one special character, but your bank requires a password of at least 6 characters that must include at least one uppercase, one lowercase and oner numerical character. Then, one web site you visit only allows a 4-character password, all numbers, and an application you use requires an 8-character password, but doesn't allow numbers or special characters.
Not only can you not use the same password in all instances, you end up with an increasing number of unique passwords to try and remember. And, that doesn't even address the fact that many of these passwords also have unique usernames.
Creating secure passwords and remembering which combination of username and password to use with a particular site or application can be very difficult. Often, there are security settings that will lock the account after too many failed attempts and force you to call for support to unlock your account or wait some specified period of time before you can try to log in again.
There are a number of tools available to help you securely store and remember your passwords and usernames without keeping a cheat sheet in your wallet, a list in your desk drawer or yellow sticky notes on your monitor. Check out the links below for more details: