At work I have passwords to eight different systems. I keep them in a file for reference as there is no way in the world anyone other than Rain Man could keep track of them, especially when they have to contain numbers, punctuation symbols, no dictionary words, and that they all expire at different times and have to be changed and cannot be repeated from previous passwords used. I have gone through all the names of cats past and present, so now I am using rock band names for my passwords at work, which gives me an almost endless source to draw from.
At home I only have three passwords to worry about, and these never change. I have another ten passwords that belong to various web sites that I log on to, such as this one and web sites where I pay my bills online.
I have a few dozen passwords. Most of them I manage to remember or can easily narrow down (my trick: old addresses of mine altered with special characters, like 123F*keStr&&t), and on websites I make liberal use of the “Forgot Password” link.
For a few work-related websites – badly designed, worse implemented, overly complex, punishment for all – in an office drawer I have a file folder labeled “Passwords – Top Secret.” 
I took a minute to count the passwords I have on one project, and it came out to 106. I have multiple passwords on multiple systems, so I’m sure the total is over 200. I keep track of them by entering the system name as a contact in Outlook. I should use something more secure, but I’ve yet to find something that I can get to from various locations, plus I can sync it onto my PDA.
I’ve got three basically, with variations. One for non-critical stuff such as here, another for moderately critical stuff like my email, and a third for banking and the like. Recently, I’ve started adding a unique “seed” to each one: a few characters at the end that’s unique to each site and something easy to remember. For example, my password here would be something like “lowsecuritypasswordSDMB”.