There is a very active movement throughout the internet to have an open standard for logging into websites that are not linked or tied into each other in any other way than the sign-up/sign-in process.

It's called OpenID. If you sign-up for an OpenID, then any website that supports OpenID will let you authenticate through your OpenID link.

As an example, I use MyOpenID.com The great thing about this service is that I own a domain for my family and I can integrate the authentication URL into my domain.

It is completely secure, because when a website asks for your OpenID, you give it a URL and MyOpenID then handles the authentication, and passes you back to the website with a command that the website says "this person is who they say they are" and log's you in.

You can create multiple profiles with MyOpenID, so if you wanted to sign-up for certain websites with your work email/phone number, and some with your home email address, you can do that all on MyOpenID.

To show you that it's completely safe, I can even give out my OpenID URL. If you tried visiting it, you will just see my name and any other info that I chose to share with the public, if you tried using it to log-in somewhere that supports it, you will be asked to MY OpenID credentials (log-in/password - which ends up being the same for all sites that support OpenID), so I have no problem giving our my OpenID url OpenID.theAustinFamily.us/Robert

Some really popular websites are supporting the movement too, like Yahoo, and I believe Google, though I don't know if they are allowing sign-ups/ins with OpenID's yet, some of them are becoming Open ID "providers" like MyOpenID.com The great thing is, you only have to sign-up for one, and then you can use whichever provider to log-in to Yahoo or Google, eventhgouh they are providers themselves.

Here is a list of websites that suppor the OpenID standard - of course, this list is only a list of ones that either are registered at MyOpenID.com or the MyOpenID website has found themselves and added into their directory (like Google, and Yahoo - I'm sure these guys are too big to worry about registering in some directory like this, but I'm sure they're listed)
https://www.myopenid.com/directory

One of the nice things I like about MyOpenID is the integration with my custom domain/website. I can allow family members that aren't in my household (my parents, my brother and his wife/kids, etc.) sign-up for their own URL and we all get to use a "vanity" URL that has our name right in it (easy to remember).

One other thing that I should mention, since you brought-up Facebook in this question, is that Facebook itself is setting itself up to provide authentication for websites that choose to allow users to "connect using facebook". One example that I use is all the Zynga games that are popular on Facebook (Mafia Wars, Dragon Wars, Space Wars, Fashion Wars, etc.) Zynga's website itself has a support forum where (much like Mahalo answers) you can ask or answer other users questions. You can use your Facebook account to sign-in/up for a Zynga forum account.

You can certainly add links to your favorite pages from your Facebook page to have them all in one handy place, but for Facebook to save your usernames and passwords for them would be a serious security issue.

Firefox and IE both allow you to save your usernames and passwords for any site that needs them, and can fill them in automatically for you. You can also download and install the Google Toolbar which has an autofill feature for any logs ins and forms.