Specifically for Web use, I highly recommend Xmarks. This add-on program for most of the major Web browsers-Internet Explorer, Chrome, Firefox, and Safari-not only can securely track your passwords for you, it also lets you keep a common set of bookmarks for all your computers. I started using Xmarks because of this latter feature, but as time has gone on I've grown to appreciate its password management functionality.
No matter what you use though the point for keeping passwords useful is to both make them easy to use and secure. If you neglect either part, you might as well forget about securing your systems. Only by balancing ease of access and password strength will you be able to keep either your own, or your company's, PCs safe.