I use Keepass. There are probably friendlier ones out there, but this one is free and it works for me on PC and Android.
I keep its password database in the cloud, and I have it set up to require both a local keyfile (which I have a copy of on my home desktop, work desktop, laptop, and phone – I don’t keep it in the cloud) and a Diceware passphrase that is memorable if nonsensical.
Setup is kind of a pain, but in practical use, no matter what website I’m at, I hit a hotkey to login, and depending on how long it’s been, I have to retype my long passphrase. On the phone it’s a little less smooth, but rarer that I have to do it.
