I just use KeePass, and Syncthing to automatically sync its encrypted password file (and other files I care about) to my android phone and all my windows computers. No cloud needed.
I second KeePass, but use a special dropbox account to sync. It does use a third party provider, but I hope my specific setup is uncommon/customized enough to defend against drag net attacks. The benefit is being able to access my passwords even after losing access to my current devices.
Not as simple as just using Dropbox, but it's probably simpler than you think. Was using LastPass and configuring Syncthing (on Windows) seemed daunting until someone here on HN mentioned SyncTrayzor. Syncthing runs as a Windows Service and you access it through a local webapp; SyncTrayzor wraps it into a much friendlier tray/desktop accessible app.
