Stateless Passwords - I've looked into those in the past and they are brilliant. There are a good number of these, perhaps the most widely used is Hashpass but there are tons of options.
My main concern with this method is if the hash method becomes compromised then your entire password structure will fall. However unlikely that would be. The other issue I find is the inability to store login names. So you must remember every login name for every account. If you are anything like me, I don't have the same login name anywhere - which adds a bit of security - albeit slight security to the mix but means I literally could not ever remember all of my login names. With these hashing systems you'd need to at least remember those.
A technique I started working with years ago is a decoration method using hashed stateless passwords in combination with a password storage/manager method. This provides ultimate security because even if the password manager is compromised they don't know your password. You simply 'decorate' the stored password with either a known decoration method, or a hashed decoration method then APPEND that to the password entered by your password manager. Does that make sense? Allow me to explain a bit better..
Let's say your password for Amazon is stored in your password manager such as:
Your password manager fills in all of that but doesn't AUTO-ENTER. So you tab up to the password entry and enter your private - memory held decoration. So in my case I could be using a decoration of 'EGD$8121'.. So I would append my top secret decoration to the password then login to the website. The decoration is NEVER stored anywhere. So the login becomes;
(1) Stored Password (2) Secret Memory Held Decoration
If you want to ramp this up, simply use a HASH tool to make unique decorations for each website! So for example using the above technique but ramping it up using a stateless password system, in this case Hashpass, I would create a hash of Amazon.com with the keycode: Biff!, which would generate the hashpass of +q99Gt2Al2gjUphY Now THAT would be my decoration in this case, otherwise known as:
This little gem has been a technique used in some counter intelligence circles for a couple of decades now. Something you have stored, something you know and something you don't know. Good luck breaking that system, right? Also, imagine if a password manager utilized both methods to generate AND insert decorations on the fly via a popup?