As someone who used to do this, yet fully (
IMO) understands the risks and issues involved, i'd like to give my reasons.
Firstly, my work-based machine requires 5 different passwords (1 for Novel /Windows logon), one for data recording system, 1 for my browser-based work email, and 2 others for apps that we use. Each of these have a time-limit on how long we can use them (which is good) and each doesnt allow a previous password to be used (also good). The problem is that each of them expire at different times (varying between 4 weeks and 6 months) and only 3 of them allow the user to change
in advance of this timeframe without admin intervention, therefore they all become different very quickly. I try to use a couple of 'core' passwords, with varying extensions (which is all that I write down, not the whole password) to be able to use the systems.