I use PasswordSafe which is open source, and I have it backed up to my dropbox (so my phone can access it). It is less convenient than most of the password managers out there having browser plugins that will automatically fill in your password, or generate one right in the text box, but the data is mine.
I still have to rely on the mobile app which isn't open source, but it is the recommended app from the main developer.
I still have to rely on the mobile app which isn't open source, but it is the recommended app from the main developer.