I'm responding before reading any other posts so as to not influence my thoughts and make them genuine.
With 6 million people still left scattered around the Earth... I'd try to have sex at least once before dying ...
Other than that, I'm not sure. It depends a lot. I'd probably bust into a Barnes&Noble and read every last book, and then I'd bust into a Borders and read every book that Barnes&Noble didn't have, and then I'd bust into all the local bookstores and read all of them books. You get the idea.
You know, there is some proof that a cladogenic event has happened to human beings like this before, and we rebuilt. I don't remember what exactly that evidence is, since it was something that I learned in my last biology class... but I'm most likely too lazy to look it up. One thing that I can say is that I was watching a documentary on the Discovery Channel about the world's largest volcano in history, which is now a city in modern day (I'll be damned if I can remember the name of the city though), and it is thought that the eruption of this volcano could be the cladogenic event that killed off nearly 70% of the human population at the time. Maybe all of this is already mentioned in a post above me... if not, here it is.
EDIT: Just for the hell of it, I'm also going to assume that I can suddenly live forever, assuming that I don't accidentally kill myself. This puts me in mind of Lazarus Long (Heinlein fans know who I'm talking about). Lazarus Long is such a kick ass character, I'd strive to be like him. So, here's a list of stuff that I'd do if there was 6 million people left and I could live forever:
-Have lots of wild monkey sex
-Create/participate in giant outdoor orgies
-Become a master of every subject so that I, along with the rest of my fellow 6 million people, could start rebuilding the Earth.
-Learn how to fight
-Get into a lot of fights to toughen myself up
-Write a shitload
-Probably keep a journal and write everything down, even insignificant shite
-Of course, try to find other people
-Create my own country (calling it a state sounds too crappy; Country sounds more sovereign and powerful)
-Learn every language and encourage others to do the same
-Make every language the official language (you know, to encourage people to be really eclectic with langauges). I think this'd be really awesome, 'cause right now you got mixes of languages like Spanglish and umm... well you know. Wherever there is a community of people who are fluent in more than one langauge, it becomes inevitable that they start mixing them. Imagine how freaking cool it would be to live in a country where everyone knows almost every language. In perhaps 100 years you'd get a few languages that are the result of mixing all of the Earth's languages (or maybe even one central language that is the result of mixing all of pre-existing languages)
-Invent my own languages
-Create a centralized internet. I'd have a whole city just dedicated to housing servers. It'd be an uber City of Computers... or something.
-Write lots of cool programs in every programming language (I'm already in the process of programming my own forum in PHP that is actually useable already
)
-Write my own programming languages
-Write my own OS
-Learn how to build boats, and build lots of them
-Get into really good physical shape
-Read every religious text ever written several times to become fluent in their ideologies and what not
-Be an awesome leader by setting examples (6 million people need a leader, right?)
-Have lots and lots of kids... with different women >.> (okay, so I probably wouldn't be able to do this if I wanted to lead by example... or I could make it socially acceptable to have lots of kids with different women ^_^)
-Drive lots of fancy cars. I'd especially want to drive a Nissan Skyline, and then a McLaren F1, and any other super-fast F1 cars. I'd also want to learn how to drift (you know, like in that anime Initial D)
-Build my own house. I'd blast down a whole neighborhood and clear away all the ruins so that I could build a super-massive mansion. I'd of course make sure that no one was living in any of the houses first. And I'd invite as many people as possible to come live with me. We'd have several out-doors pools and what not.
-Push for space exploration. I'd gladly give up my post on Earth just to sail amongst the stars for the rest of my life, regardless of the cost or the risk involved. I'm a lot like Heinlein in that I want very badly to be able to explore the stars within my lifetime. I love watching anything related to space, and reading about stuff that's out there. Unfortunately, I don't see this actually happening even within my lifetime.
-Rebuild the Tower of Babel
-Build my own pyramid the way the ancient Egyptians did.
I'll stop here since this has gone way beyond the realm of the original post.
EDIT2: Yes, I did take some time to read about 80% of all the posts above after my initial post.