No story here but the story you make for yourself.
One is called UnReal World. It's a roguelike... ever heard of those? They were the first type of rpg that took place in randomly generated worlds. Anyway, it's a roguelike where rather than taking place in some fantasy setting where you're an elf wielding a sword +1 fighting goblins, you're just some poor sap out in the wilds and forced to survive. You create a character and choose from stats which will affect your survival such as whether you know how to hunt with a bow and arrow or if you know first-aid and such, and then play that character in the inhospitable wilderness trying to survive.
It's possible to even find towns, trade for supplies, buy or build your own house and even eventually settle down and start a family... of course none of my characters have ever made it that far. Typically they end up bleeding to death or starving or suffering some other horrible death thanks to my unskilled hands. And ya know what? THAT'S GREAT! You know how fun it is to tell stories between me and my buddies about how my latest poor sap met his end? It's fun, and you're learning the entire time too. Some day... maybe... I'll actually survive to build a family in the game.
There's a score chart to show off how well you've done too, so survival, while possible, isn't always the most fun goal.
Link: http://www.jmp.fi/~smaarane/urw.html
The other, and by far one of my all-time favorite games, no lie, is called Dwarf Fortress. It's somewhat similar to the above except that it's got an amazing strategy twist; You're not just playing one character, you don't control anyone at all. Instead you're started off in charge of seven dwarves (Get it? Hur hur) and left with the responsibility of establishing a colony. Seven Dwarves and a cartload of whatever supplies you choose to bring, that's all ya got.
If you've ever played Dungeon Keeper, or Evil Genius, or any other game like that then you'll instantly be familiar with the setup. You need to dig deep, build halls for housing, set up craft-shops for building furniture and supplies. You need food and water and safety; There are enemies aplenty in the game and if you're caught unprepared it's possible a goblin raid will slaughter your fledgling fortress, or wolves will butcher your hunters, or any other of millions of possible situations. Cave-ins, plague, disease and famine. This is another game where failure is at first inevitable. But it's fun and as you keep playing you'll eventually figure out how to set up traps and death-pits, proper food chains and shops, till you're controlling a fortress with hundreds of dwarves and perhaps even become the new Dwarven Capital as the King moves into your fortress (I've yet to have had that happen, but it *is* possible)
What makes it all worth-while is that every dwarf plays like a tiny Sim, with their own likes and dislikes, their own personalities and goals. They'll get married, have children, throw fits and get in fights. It's amazing to watch em all interact with each other and grow.
This one's also free: http://www.bay12games.com/dwarves/
Enjoy! Be warned however, once you get into em, both these games are major time-sinks. I dare not try and count how many hours I've spent trying to build the perfect Dwarf Fortress...
And good luck. Neither is exactly newbie friendly, but once you figure em out you wont turn back. Took me forever to learn Dwarf Fortress, but there are guides available so if you decide to give em a try msg me and I'll send you a link or two.