LastPass is a cross platform password management that works in all operating systems and smartphones. Basically, it is a browser plugin that offers to save passwords and automatically fill login details with data saved.
Using LastPass is secure because only you have access to all data stored, using a master password.
Is highly recommended to use different passwords for different login gateways or sites. If you loose one password, you will compromise only one account. Also, is recommended to use strong passwords instead a simple one because can be easily guess by typing or with a dictionary database.
With this application you will be able to create and use different and strong passwords for each website and automatically login without needing to fill each password. This can be time saving and, in fact, more secure.
Do not save passwords in a text file where anyone have access or can be stolen by a virus. Instead of this, save them in a secure area where only you can add/edit/save data with a master password. Below is a list with apps or programs like LastPass.