If this doesn’t convince you to use a password manager just look at it this simply. We are seeing more and more hacks aimed at grabbing passwords from random websites, not so much to get access to those accounts, but to try and run the same usernames and passwords over other websites and gain access to those accounts. For example, the LinkedIn breach contained some really old data, but how many people were using the same combination on banking and other sites? Turns out, enough to make it worth while for hackers to get that data.
So, really, to protect yourself from that, you should never repeat passwords across different sites. Good luck remembering all the passwords you have setup! There’s no way.
Personally, I use LastPass, but there are other options out there, and you should really be thinking about it.