The reason why you should never reuse your password across sites is because if one of the sites gets hacked the attacker will try that same username and password across sites and gets in all of your accounts. It is impossible remember all the passwords one has, that is where these free password managers will help you, some of them are cross platform and can be used in Windows as well as Linux.
KeePassX: This password manager encrypted database can be passed along Linux, MAC and Windows computers, the software is compatible across all platforms, your database can be opened in any computer regardless of OS. KeePassX will save user names, passwords, urls, attachments and comments in one single database encrypted using AES 256bit.
Password Gorilla: It runs in Linux, MAC and Windows, if you decide to change your computer OS next year it will not be a problem, Password Gorilla encrypts the database with the solid TwoFish algorithm and SHA256 for password hashing, it makes for a good alternative to KeePassX, both of them have portable Windows version that can be used from within a memory card or USB thumbdrive.
Password Safe: Multilingual open source password manager for Linux and Windows, a U3 and portable version are also available, it uses Twofish and SHA-256 for encryption, other related projects implement Password Safe in Java, a command line utility called pwsafe and PwSafe for the iPod, iPad and iPhone Touch, you can get support for Password Safe on its website discussion forum.
Alternatives to the password managers mentioned above that work across platforms are web based password services like LastPass and PassPack, but I strongly discourage you from using those because anyone with access to your browser can have access to your passwords and because man in the middle attacks are also possible in web based password managers.