freitasm:
LastPass. And make sure you activate 2FA - on LastPass itself and every other site where you can. And use Authy because it syncs 2FA tokens (or LastPass itself). Do not use Google Authenticator because if your phone is gone, it's gone.
I had this problem with Google Authenticator, where my phone died. But I found I could disable 2FA in lastpass, and then was able to access it without 2FA. Then I could setup Google Authenticator on another phone. In a way it is a bit of a concern you can disable it to do this though.