This is a secure password generator that doesn't store any information whatsoever. Using this site, you don't need to use a "password locker" or anything else that might lose your passwords. You can save it to your own computer so you have access to it even if my website disappears; it's a single-page, totally self-contained app, with the only external file being a small script to make it available when you're offline.
To use, first come up with a secure "Master Password". This can be anything you want, but it needs to be a really good password: random letters and numbers, decent length, the whole jazz. Write this down somewhere secure until you memorize it; if you forget this, you won't be able to access any of your passwords. You'll use this Master Password for all your passwords; it's the only secure password you'll ever have to remember again.
Then, whenever you need a new password for something, come up with a "Password Name" for it. This should not be secure and random; it should instead be easy to remember later. For example, if I need to make a password for my Google account, I can just use "google" as the Password Name.
Then hit "Short" if you want a 12-character password, or "Long" if you want a 26-character password. Most websites will accept a 26-character password, and it's vastly more secure, so use that whenever you can; the 12-character option is for the occasional badly-written site with maximum password lengths.
Every time you use the same Password Name and Master Password, it'll generate the exact same password, so you don't need to write down what it generates. Just memorize your Master Password and keep your Password Names easy to remember (and write them down somewhere, too!) and you can get your passwords from anywhere.
If the Short and Long buttons don't work (some sites are really badly designed and have asinine requirements on what your password must contain), click "More Options" and select exactly what you need: whether the password requires digits, punctuation, or uppercase letters; whether it needs to have no punctuation or be only digits (for a PIN number); and what length you want. Then click "Generate Custom" to get your custom password.
I recommend saving your Password Names somewhere you can easily access them, in case you forget. These do not need to be secure, so feel free to use a notebook, or a Google Doc, or anything else like that. This will also let you record if a site had special requirements for their password that required you to use Short or custom options, since you need to set the exact same options every time.