While there are alternatives inside firefox itself, I strongly recommend using two free add-ons, which really make your life simpler.
The first one is LastPass, an add-on which stores all your passwords, generates new ones of arbitrary complexity when needed, capable of logging you into a site automatically when need arises. Your passwords will be saved, in an encrypted form, on their server; the password needed to decrypt them is stored neither on your pc nor on theri site, so that an attacker will come out empty handed. That password is the Last Pass referred to in their title. The app is cross-platform (i.e., it works on all versions of Windows/Mac/Linux), and cross-Browser (works on IE, Firefox, Chrome, Safari, Opera,...). It also synchronizes your password database across multiple installations all belonging to the same user instantaneously. So long as you stay away from their cellular phone version (Android, iOS, Windows), it is also free. On first installation, it will sanitize the local repository of passwords, making them very safe. Their Web site is here.
The second one is Xmarks, also a free add-on that synchronizes your bookmarks across different pcs. Like LastPass, it is both cross-platform and cross-browser. It also has the capacity to synchronize whole sessions, so that, if you tomorrow morning wake up in a different house, different city, different country, you can pick up exactly where you left off. It also supports multiple profiles (work, fun,...) so that you may have access to completely unrelated saved sessions. This is their Web site. Once again, their business-plan is to charge only for applications on cellular phones. Needless to say, both applications function as back-ups.
When I have a new pc, these two are the very first apps I download, because they help me feel at home immediately.