I'm a big fan of the Keep It Simple (KISS) approach, and went with Password Safe. Works on Linux, Windows, MacOS, iOS, and Android. It's big thing is it just makes an encrypted password file which then you can sync between devices however you like (Box, Dropbox, etc)
Which one works on all browsers including mobile safari and mobile Firefox?
It has an auto-type and copy feature, so no need for browser support. Though, the main criticism of this offering is if you want a ton of features and don't care about KISS.
Pedant thought: The thumbnail shows one biting everywhere but the bullet.