Ask HN: How do you manage your passwords?

Perhaps I'm just more aware of it, or perhaps it's happening more frequently, but it seems like every couple of weeks a major service demonstrates that they have exposed some user data or passwords.

Intellectually, I know I should be using a different password for every service, game, and application I use. Practically, I reuse a handful of long, strong passwords.

I'd like to change that practice. I'd like to use a different password on every service, but that's probably a few dozen passwords. Too many to remember practically, in any case. There's a lot of misinformation out there about how to do this correctly, and I'm looking for examples on how to do it right.