Everyone has issues keeping track of all their passwords, but the issue is double-fold for IT staff. You not only have a need for your own passwords, you have to remember administrator passwords for a large number of systems. There are many applications out there that will do this password management for you and all of them have their up sides and down sides.
The way that I have managed passwords over the last 5 years has been through an application called KeePass. KeePass is a free open source application that stores you passwords in an encrypted file. You can put notes and other information into KeePass as well. It allows you to group like passwords together in groups you can define. I do things like work passwords, bank accounts, support sites, social media accounts, etc.
There are KeePass applications for lots of different OS’s as well. Apples OSX, the iPhone iOS, Microsoft Windows, Linux, Android, etc. Keeping your encrypted files synced between all these devices can be a bit tricky, but it is a great start and has seen me through thousands of passwords over many years.