SpaceSimCentral

Age of Ascent
Age of Ascent is an epic 3D space MMO that runs natively in your browser without downloads, installs or plugins. It's been built from scratch in a completely new cloud-based architecture - and that means that thousands of players can battle concurrently in realtime, without sharding or slowing down the server clock. We have free alpha playtests every Saturday, so please come along and see for yourself!
Homepage: AoA Homepage

Elite: Dangerous
Elite: Dangerous is the latest installment in the Elite series of games. This will be the first sequel that isn't using 80's gfx technology.
Homepage: Elite Dangerous Homepage
Purchase from: Steam
Status: Online

EVE Online
As of right now pretty much the largest of all the Space MMO's out there, but that might change shortly. In EVE it is more of a corporation building game and doesn't have twitch based combat.
Homepage: EVE Online Homepage
Purchase from: EVE Online
Status: Online

Infinity: Battlescape
Infinity: Battlescape is a multiplayer space sim involving hundreds of players split across three competing corporations of the Starfold Confederacy fighting for control of a procedurally generated, true to scale solar system filled with planets, moons, asteroid belts, and other celestial phenomenon.
Homepage: Infinity: Battlescape
Status: Under Development

Outspace Game
Outspace is 1,000,000,000,000,000 Kilometers of space where you can develop gigantic space structures, colonize planets or build own army to dominate other players.

Star Citizen
Star Citizen is not just an Multiplayer game, it will also contain a single-player game (Squadron 42) which will put you into the persistant server for multiplayer when it is completed. Star Citizen is a game being worked on by Roberts Space Industries. This EPIC game will be released in 2014.
Homepage: Star Citizen Homepage
Status: Under Development

StarTrek Online
Yes it is finally happening a MMO based on the Star Trek Universe. You will be able to play several races from the series and create your own race. You will be a captian of a starship to explore and fight in the Star Trek Universe.
Homepage: Star Trek Online Homepage
Status: Online

Vendetta Online
Vendetta Online is a open ended, skill based character driven system which allows users to pursue their own direction. While some of the story is pre-scripted, it still allows for great variation depending on the actions of players.
Homepage: Vendetta Online Homepage
Status: Online