The big problem with random passwords is when you don't have access to the tool maintaining the passwords (i.e. they are virtually impossible to remember so either software has to store them or you have to write them down).

The alternative (easy to crack passwords) is worse. The problem is that many programs/sites won't let you use passwords that are easy to remember, but hard to crack. That is, they won't allow passwords long enough to use effective "pass phrases". A semi-random string of words is almost impossible to crack, but not hard to remember if you use appropriate mnemonics. So you use a good pass-phrase to control access to the password store, and short but hard to remember passwords for the actual sites.

I know with 1Password and DropBox, I can get access to the password store on any computer with internet access, even if I don't have the tool, if I'm really stuck. And if I don't have that access, I can't imagine any scenario that I would actually need the passwords.

joe