EVE Online

I chose EVE because of it's complexity in both it's gameplay and background, single unsharded server with no instancing, skill training system, and my corp

Gameplay wise you are in space making a living in various occupations you can think of. You can be Mission Runner, NPC Hunter, Miner, Manufacturer, Researcher, Trader, Hauler, Security, Pirate, Smuggler, Mercenery and combination of whatever is possible. How you created your character you initially meant to be, you can be whatever you want to be later.
Primarily I'm a Mission Runner, alternating a Miner, Hauler or Security in my corp's Mining Ops. I'm a Combat Pilot (for now PvE only) by heart but that doesn't stopped me from doing other jobs

Basically EVE made up of 4 playable Races or more commonly as Factions, Caldari, Gallente, Amarr, and Minmatar. Each Faction have their own specialized ships. Note that any other Faction can pilot other Factions' ships, provided they have the required skills (no whatsoever penalties are involved). The only reasons which Race you chose (that I can think of) mainly because each Race have their base attributes you wish to start out with and maybe for the Race's identity. Lookie here for example of the Races' base attributes: EVE Online Player Guide: Character Creation
EVE Online's ongoing story and happening rarely affect me, but it's interesting to see there actually something happen. Most interesting is there are events by the developer (CCP) such as puzzle solving to inherit some of a deceased Billionare's wealth, and GM Pirates raid on major Alliance's POS (Player Owned Structures).
PvP and PvE (Player versus Environment) are in the same universe, only differentiated by security rating of a star system. Star systems rated as 1.0 to 0.5 is High Sec(urity) which pilots that do not wish to involve in PvP resides in. While 0.4 to 0.0 Low Sec systems are PvP haven. In High Sec space, we "Carebears" (term used for those who do not want to involve in PvP) are protected by Concord, the space Police . In Low Sec, everything goes. A Corporation (equivalent to a guild) in an Alliance can construct and maintain a POS for Low Sec activities.
In EVE Online, when your ship destroyed either by rats (NPC pirates) or Pirates (player pirates), you lose your ships, fitted modules and whatever in your cargohold. Your lost ship will be compensated by insurance in ISK, provided you bought one in the first place. Some of your modules may survive, to be looted by Pirates or by you (when in Mission running for example). After your ship, you will be in your Escape Pod, which can be destroyed or "podded" by Pirates (but not by rats) leaving you revived in your clone. Your clone is sort of your character "save files". Make sure to update your clone by buying a new clone with higher capacity to retain your skills, and buy new one when you are podded because you are your clone. Creapy huh?
Fun eh? You gain, you lose. So does your foes Fun and sad are shared all around
A more comprehensive explaination of EVE Online background:
Wikipedia - EVE Online
EVE Online Player Guide: About EVE Online

Aye, single unsharded server with no instancing. This I like, the universe I'm in won't miss any actions that might happen in other server(s).

Skill training. The attributes I talked about determine how fast I can train a skill. A skill have a primary and a secondary attribute. Attributes affect how fast a skill can be learned.
Skills are not trained by means of leveling, but are trained real-time. Skills are bought, training one skill at a time and only when that particular skill is activated to train.
This served me well, since I don't have that much time to level all day long. I won't lose in term of uberness of my character, only lose out in wealth. This I can live with
The time you spend in EVE is to gain ISK (EVE monetory). Well, ISK is everything (like in real world ). How would you want to pilot a Battleship, when you only have the skills but not the ISK to buy one?

Sorry for rambling this much and hopefully nobody lost with what I said here
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Lowyat.NET: EVE Online thread