If you're using a password manager, that's a non-issue. And until we have something better than passwords, you really should be using one.
What's important is to keep a backup of your password database in a few places. I use KeePass because I have no desire to keep passwords, encrypted or not, in a cloud service. I also don't find value in browser integration (possible attack vector?). I'm generally very DIY-inclined anyway. Your preferences may vary.
As a full disclaimer, there are some issues with KeePass [1], but known issues are detailed in full by the project and are available for review.