KeePassX stored on Dropbox works very well for me. I can access on multiple devices, my phone, my laptop and my work PC. Yes it all relies on a master password but it works well for the level of security I want.

Then there is my wife's strategy 20+ char passwords with a mix of numbers and symbols. She uses unique passwords for everything and the only place they are stored are in her head...

Meanwhile I manage to forget my own age.