Depending on what you are planning to do. If you want to store your browser passwords, you should look up services like 1Password. If you want to store your passwords for everything else and don't need automated fill-ins, I would recommend a Truecrypt container with a text- or excel file in it. You can store it wherever you like (S3, Dropbox, etc.) as long as you decide to use a strong password or keyfiles.
Thanks for your answer. Using Truecrypt and saving it on Box.net or Dropbox was an idea I also had. This cheap solution only has the problem that anyone who gets access to my cloud hosting area could find that Truecrypt container if it isn't cleverly hidden or disguised. And that master password has to be very very long and very complex, as I learned from Ars Technica:
Finally here is a interesting aspect which I just found here in the comments of a Dashlane review:
Quote: "David Pogue (NYT) raved about Dashlane, too, so I took the plunge. Immediate problem was that my login information wound up permanently entered in one of my credit card sites; it was an auto-login I could not disable. So if someone DID steal my laptop, it would be a happy time for him. Trashing Dashlane had no effect; I had to do a force quit of the Dashlane agent using Activity Monitor, then trash it and other attendant files. So many of these password managers, including the incredibly wonderful 1Password that everyone swoons over, imbed themselves so deeply into browsers and other functions that I don't trust them. I will stick with Password Wallet, which sits isolated off to the side and doesn't try to do too much. I understand it and am less likely to make mistakes."