What would you spend the next billion (billion billion billion billion billion billion billion billion etc.) years doing?
This is assuming:
-You have perfect memory, and remember everything.
-It is impossible for you to die. Your body regrows lost limbs, your organs never fail. But you can still feel pain.
-You have eternal youth.
-Your brain is invulnerable to things like mental diseases and going crazy. You'll always be sane.

I would become skilled at everything ever, and become some sort of super awesome human library of knowledge.

post on stickpage

In my first 100 years, I would learn every single piece of information in the world. Using that information, I somehow become king of the world. Then, I'll somehow suddenly become a tyrant and do evil shit like genocides and stuff. Then I'd suddenly disappear for a few thousands of years, giving people a false sense of security and making them wonder if I ever existed. During those thousand years, I train my body in every single martial art in the world + learn how to make weapons and heavy machinery. I build one fuck of a giant mecha and terrorize the city, and tell everyone that I'm immortal. I'll create mass destruction with the said robot, then eventually let them capture me. Without a doubt, they will obviously try to execute me, but I'm immortal so I live. Seeing that it doesn't work, they'll give me a life sentence, then, using the skills I've acquired over the years, I break out of prison and go in my second mecha and kill more until they recognize me as king again. Then, for a few hundred years, I show myself as a nice king, then do evil stuff again.

I'd, besides learn everything there is to know, join the military and become the most efficient killing machine imaginable. Then, I would stage my own death and become a psycho-vigilante killing machine that roves the planet assassinating dictators and corrupt senators.

I would have an alias and everything.

Where do I sign up?

Quote from Animage

In my first 100 years, I would learn every single piece of information in the world. Using that information, I somehow become king of the world. Then, I'll somehow suddenly become a tyrant and do evil shit like genocides and stuff. Then I'd suddenly disappear for a few thousands of years, giving people a false sense of security and making them wonder if I ever existed. During those thousand years, I train my body in every single martial art in the world + learn how to make weapons and heavy machinery. I build one fuck of a giant mecha and terrorize the city, and tell everyone that I'm immortal. I'll create mass destruction with the said robot, then eventually let them capture me. Without a doubt, they will obviously try to execute me, but I'm immortal so I live. Seeing that it doesn't work, they'll give me a life sentence, then, using the skills I've acquired over the years, I break out of prison and go in my second mecha and kill more until they recognize me as king again. Then, for a few hundred years, I show myself as a nice king, then do evil stuff again.

they totally won't waterboard you for a couple thousand years.

Hmmm, interesting. I guess I'd start off by living the same way as I am right now until I get bored, and then afterwards, I'd experiment a lot and try out a variety of things, such as gaining knowledge as Devour said, or trying to be different kinds of people. I would also work myself up to become some sort of demigod, for further experimenting purposes. Perhaps if I reach a demigod's power, I can also find some sort of way to stop myself from feeling the emotion of boredom, or at least make what used to be boring not boring anymore.

Quote from Devour

I would become skilled at everything ever, and become some sort of super awesome human library of knowledge.

I'd like to think I'd do this, but even now when I have limited life span I can barely push myself to learn the stuff I'm interested in. I genuinely believe I could procrastinate away an entire eternity.

Learn every language in the entire world, form my own country, and make all of the laws subject to my immediate demands. It would be so funny.
I'd also work endlessly to find the secret to creating life, form my own species of bacteria, and launch me and the bacteria culture off to a distant planet (I could easily get the resources for this since the government would know I'm immortal by now) and form a colony and just watch billions of years of evolution, ruling over those lifeforms as a literal god. If people or human-ish creatures eventually formed I would totally have sex with them.

would you still feel pain when you don't eat/drink?

Gain massive amounts of intelligence, and use that to obtain science grants and such, giving me a fuckload of money. Then spend that money building a private area where I can inquire further about things, learn skills I want, and just do whatever.

Quote from Animage

In my first 100 years, I would learn every single piece of information in the world. Using that information, I somehow become king of the world. Then, I'll somehow suddenly become a tyrant and do evil shit like genocides and stuff. Then I'd suddenly disappear for a few thousands of years, giving people a false sense of security and making them wonder if I ever existed. During those thousand years, I train my body in every single martial art in the world + learn how to make weapons and heavy machinery. I build one fuck of a giant mecha and terrorize the city, and tell everyone that I'm immortal. I'll create mass destruction with the said robot, then eventually let them capture me. Without a doubt, they will obviously try to execute me, but I'm immortal so I live. Seeing that it doesn't work, they'll give me a life sentence, then, using the skills I've acquired over the years, I break out of prison and go in my second mecha and kill more until they recognize me as king again. Then, for a few hundred years, I show myself as a nice king, then do evil stuff again.

You learn martial arts, but you're not super human.
If they recognized your immortality and contained you in a large and thick concrete cell, I'm sure you would have a very hard time breaking out. Even though you regenerate yourself, beating the shit out of the walls probably wouldn't work very well considering you still feel pain. Besides, what if they hooked you up to some sort of gigantic pendulum blade (Like in one of the Saw movies) that constantly cut off your arms and legs. Dang I feel sorry for you.

Considering the type of person I am, I would have a family and enjoy my life with them until they passed. I would then most likely journey the world and learn as much as I could. Probably after one hundred years or so, whenever society and technology has prevailed enough for deep space exploration or colonization of another planet are realistic ideas I would sign up with the most technologically advanced space organization at the time to journey the galaxy. I'd probably live long enough to see if a time machine would ever be constructed and once it is I would journey back in time to see which religion was correct. I would then most likely get my family and bring them to whatever present tense I would actually be in and spend the rest of their days with them. Once they pass I will most likely crave mortality. If Christianity was the correct religion, I would most likely ask for forgiveness as I pilot my space shuttle into the sun. Immortality is great and all, but life would be boring after a while.

Quote from Fusion

Learn every language in the entire world, form my own country, and make all of the laws subject to my immediate demands. It would be so funny.
I'd also work endlessly to find the secret to creating life, form my own species of bacteria, and launch me and the bacteria culture off to a distant planet (I could easily get the resources for this since the government would know I'm immortal by now) and form a colony and just watch billions of years of evolution, ruling over those lifeforms as a literal god. If people or human-ish creatures eventually formed I would totally have sex with them.

and then create an insanely big army and invade earth.

Simply sit back and watch everything unfold itself. Watch eons of civilization grow and be destroyed. And being immortal, I would travel to witness the greatest events in history. Such as right now if I were immortal I would be in Syria witnessing first-hand the rising revolution of freedom and democracy. History repeats itself but will never be exactly the same. Thus I would never grow tired of simply observing society.

However if everyone died I would try forming a new formation of life as many have stated before. From there I'll re-witness the growth of intelligent life. I'm sure with the conditions the universe and the world have been put in, things won't end up the same. And I could laugh as I reference back mistakes to history.

Quote from Captain Cook

and then create an insanely big army and invade earth.

I'm predicting that humans would be long gone from Earth if they're still around in a few billion years.

Quote from Arch-Angel

pilot my space shuttle into the sun.

I put italics around "impossible." You'd be burning at 250,000 degrees celsius until the sun exploded, lol.

Literally Hell lol.