Can you recommend a password manager that works on all browsers/devices that you trust?
I have not found that yet, so I use passphrases customized to the site.
Edit: Also fundamentally it means that to access a single site from a compromised device, I'm potentially giving a nice list of all of my credentials.
1Password works on iOS, Android, and Mac (as confirmed by me) and they claim Windows, too. Browser-wise, I can confirm Chrome and Safari. That works for me, as it covers all of my use cases. YMMV, and it most certainly will if you're running Linux.
Downside: good $DEITY is it pricey by the time you cover all of your mobile devices and desktops. The amount of hassle it saves me probably pays for it, but covering all platforms at my house is bumping up against $100 (not including a couple of paid upgrades along the way).
It's in the Debian & Ubuntu repositories. It is also in the F-Droid repository for Android mobiles, so you can install and update easily from an AOSP ROM. All of the above are free and open-source which helps quite a bit with establishing trust. If you are among the majority using Windows or Mac it works there, too.
Sync it between devices by storing its (by default encrypted) database in a service like ownCloud or Dropbox.