Although you can use the password managers inside different browsers, it can get unwieldy if you often switch between browsers, like I do. In this case, it's very useful to have a password manager that keeps everything up to date across the different systems. The one I use is Roboform , and it does such a great job that I've never bothered even trying another one!
The good thing is that you get to use it free for 30 days, and you can continue free if you only need to save 10 logins. During the 30 days you have unlimited logins to try out. It works best with Firefox and Internet Explorer, but they do not currently support the Google Chrome or Opera browsers.
One further version is RoboForm2Go - again available with a free trial - which you can take on a USB stick and use on any computer.