EVE Online is my idea of a perfect MMO, and I wish I could play it more. But the friends I like to hang out with are on other games, so.
EVE is less of a game and more of a persistent virtual world (galaxy, really). The economy is one of the most robust I’ve ever encountered, and it is in fact possible to have a fulfilling career on the game and never engage in fighting.
That’s the key word, though, ‘career’. A lot of it is more like work than goofing off. If you get a kick out of numbers and resource management and profit, you’ll love it.
EVE takes place in a galaxy several millenia in the future, with humans having evolved into four similar but disparate races and cultures. Each of these attained spacefaring technology in their own ways, and by making use of warpgates they’ve been able to travel between solar systems. You play as a ship pilot, and it’s wholly up to you to decide how to make a profit in the game.
It’s not that the end goal is to make a profit, but to do much of anything you’ll need cash. To play with some of the bigger ships and more advanced systems, you’ll need a lot of cash. As I said before, the economy is very robust and players are involved in almost all steps of the process; there’s very few money fountains or sinks. The basic economic cycle operates roughly as such:
Miners extract raw ore from asteroid belts. They sell it to refiners, who turn the ore into minerals which they sell to manufacturers. The manufacturers create ship systems which everyone buys. Combat pilots earn money primarily by collecting bounties on computer-controlled pirates and selling salvage to other players. There’s also a few other professions who contribute to the economic cycle, such as scientists and such, but I never delved that deeply into those areas. There’s also traders, who run cargo from one station to another.
The important thing to note is that the game is not based off a class system. You don’t select Miner as your Profession when you start. Instead, the game is entirely skill-based; the better your Mining skill is, the more efficiently you can extract ore. You can learn any skill for which you have the prerequisites; the only limiting factor is time. Low-level skills can take under an hour to train up to a usable state, while high-level skills can take several months. This allows for an organic growth in your character. Mine started out as a fighter pilot, but eventually learned mining, refining, and trading skills. By the time I stopped playing I almost never engaged in combat.
The game is player-versus-player at all times. However, each solar system is rated for its security level on a scale of 1.0 to 0.0, 1.0 being almost completely safe and secure with 0.0 being utterly lawless. (This refers to computer-guided security; if a player group chooses to patrol a 0.0 sector, that area may be safe as well.) You can have a fulfilling career never straying outside the 1.0-0.8 range and you’ll never encounter someone who wants to destroy you. On the other hand, the lower the system security, the better chance of earning good rewards in combat or mining.
Player groups are known as corporations. You start in the newbie corporation, and from there you can find your own.
I think that’s really it. EVE is basically notable for involving players in every step of the economy and giving them an unprecedented amount of control over what they do in game. It’s a little spartan and can be difficult, but if you like resource management and crafting then you’ll love EVE.
One warning: the learning curve is very steep and can be intimidating to a new player. You may find it overwhelming at first.
That’s all I can think of off the top of my head, and I have to get back to work. 
