I use Keepass[1] with the Kee[2] extension on Firefox and on Android I use Keepass2Android[3]. All 3 are free and opensource.

For synchronizing the kdbx file I use Dropbox.

[1]: https://keepass.info/ [2]: https://addons.mozilla.org/fr/firefox/addon/keefox/ [3]: https://play.google.com/store/apps/details?id=keepass2androi...