In my perfect world signing up to a service would only need my email address. I'd enter it and the service would email me a link. Clicking that link would log me in. No password necessary. My log in credentials would be available everywhere my email is available (which is everywhere), and if I accidentally delete the email then just filling in the "sign up" box with the same email address would email me a new one.

The downside is that if my email account is compromised then my account with the service is also compromised, but if that's the case then most 'forgotten password' systems would be equally broken.