I use KeePass to store all my passwords on my PC. There are at least two apps (KeePassDroid, which I have been using happily for years, and Keepass2Android, which I've been trying out) available on Android which can access the same password database.
Don't forget to back up your password database - if you use a different password on every site (which you really, really should), then you don't want to risk losing your password database!
https://keepass.info/