Microsoft and PayPal, 2 organizations that store your most private information have password character limits of only 16 and 20 characters, respectively. These passwords are vulnerable enough to bruteforcing and it's possible for accounts to be compromised. I bet there are a couple of more ways to get these passwords, for example through phishing etc.

When you use a longer password you will likely have to store it in a protected file on your computer, for example using KeePassX. KeePassX decrypts the passwords for you and only grants access via one single master password for a the password file. Your own computer is a more secure location to store this, too, because:

To get access to the password without physically having the computer, the hacker needs your IP, and your computer needs to be connected to the internet. The hacker also needs to bypass your antivirus and firewall and then somehow get your master password. Make your master password a near 30 character password and make all your other passwords 256 characters and store them in the file. There are enough ways to remember a master password. Just writing it down physically is in my opinion not even too much of a bad idea because as long as it is out of sight of a webcam the hacker will not be able to see it, and he will have to crack a 32 character password on. your. computer! 

A 16 character password would take a PC quite a long time to crack, about 350 thousand years. But professional hackers often have multiple really fast pcs, reducing this time enough. I couldn't find exact numbers of the amount of microsoft accounts, but you can imagine this is in the order of a couple 100 millions. Taking into account most people at the moment don't have a 16 character password (or 20 characters for paypal) there is a good chance for passwords to be cracked. Also take into account that computers are getting faster rapidly.

A 256 character password's chances of being cracked are very near 0. Just take this from me: 256 character passwords will not be cracked. I can't forsee the future but I'm rating the chances of any computer made within 100 years from now to be able to within 350 thousand years to be very low. With a 256 character password, your personal information and money is stored safely on the internet, and this can remove some stress, too, especially for people with higher chances of being targetted by hackers.

I'd like Microsoft and PayPal to increase their character limit to 256, a good length for strong passwords. Sign the petition now if you think so too and you want to be able to store your information online safely with these companies!