Use passphrases instead of passwords.
Passphrases generally take the form of abbreviations; for example, "TQBFJOTLD" would be a simple passphrase representing "The quick brown fox jumps over the lazy dog." As written, the phrase is resistant to dictionary attacks (programs that try tens of thousands of English words as possible passwords).
You can also dramatically increase passphrases security by mixing upper and lowercase letters and including numerals and select special characters.