It's hard to keep all of those numbers and characters straight, especially since you shouldn't use the same password for more than one service. Some people store them in a document on their home computer. This is fine -- if (and only if) you encrypt the file, a feature available on most personal computers.
Encryption scrambles text, so it will be unreadable if someone hacks into your system. Even with this defense, make sure your main log-in is protected by a ''super password,'' one that has at least eight characters and a mix of uppercase and lowercase letters, symbols, and numbers.
There are other, more high-tech storage options to choose from. For example, you could put your passwords on a portable USB flash drive with fingerprint recognition. The biometric device costs upward of $100, but you'll be the only person in the world who can access its contents, because only your fingerprints will open it.
Then there are programs that you can download from the Internet (often for free) that will maintain a protected database of passwords for you.