I only know one password: my master password for LastPass. There's absolutely no possible way I could ever memorize all the passwords I have across various sites on the internet (well, maybe I could, but I don't want to). Simply put, password managers are a godsend.
If you're not into LastPass for whatever reason (or just looking for something new), it may be time to check out PasswordBox. It's basically on par with LP when it comes to price ($12/ year) and having you covered across multiple devices (Android app and Chrome extension), but as of the most recent update to the Android app, it also boasts a feature that LastPass can't hold a candle to: one-tap logins.