I've used KeePass (KeePass Droid for the phone) for years. I keep the data file on the cloud (Dropbox in my case), so that I have all my passwords on all my devices at all times. KeePass has pretty good encryption (although nothing is 100% safe), but no one's gotten into anything I keep a password in KeePass on. (It's free for Windows, MacOS, Android and iPhones.)