Some of us at DTB resisted the use of Password Management software for a very long time, simply because remembering several slightly complicated passwords seemed like a better option than having a single point of vulnerability; ie- the one passphrase on the password manager. Then LastPass got compromised and we went a little crazy for a while and refused to use anything remotely resembling a password manager.
Finally, we discovered KeePassX. KeePassX is open source, uses very strong encryption, allows you to create strong passwords from within the app, then later right-click and copy/paste user names and passwords without every having to type them (which defeats a keystroke logger). There are innumerable plug-ins, some of which allow for browser integration and synchronization across multiple machines. (Because these are open source projects and are frequently updated, we’re not going to hard link to them because as soon as we do, the url will change.) It also has mobile integration, so you can use it on your pocket device. MiniKeePass for iOS and KeePass for Android.
LastPass is still a preferred solution for many people and has full browser integration, is in the cloud so it’s easy to manage across multiple platforms, and has a very pleasant user interface, so it may be right for you.