One can, of course, program one's computer to remember many of one's passwords, but I think that is a major security risk, so I tend to turn those functions off.
There have been a few advanced security schemes tested. For example, some banks track the password, and the PC where the login attempt was made. If a login attempt is made at a "unique" PC, then the bank will send a confirmation message to one's cell phone, at which point one must type in the confirmation code into the login. Of course, invariably my cell messages didn't come through, and I ended up standing outside in the cold hoping to get my confirmation numbers.
Another method used is a "bingo card". It is quite a simple concept. One has a list of probe codes, and answer codes written on a card that the person keeps. So, when one attempts to log in, one must look up the probe question and answer on the card. If the card is lost, a new one is issued.
No doubt the future will bring more sophisticated online identity verification. My IBM/Lenovo laptop had a fingerprint scanner, but I don't think that concept really caught on.