I'm really surprised someone beat me to Starshatter - it has barely any recognition at all. And then throwing down I've Found Her in the same post - you're taking all my suggestions!
So, yeah, there's several space sim games, with different takes on the whole thing, and it depends what angle you want to play:
If you want to be in a Fighter (and you want an actual sim):
-) I've Found Her (Babylon 5 Universe, full newtonian)
-) Starshatter: The Gathering Storm (Original IP, Dynamic Campaign, arcade/semi-newtonian/full newtonian options)
-) X-Wing Alliance (Star Wars universe, arcade flight model, sim level control options)
-) X series, X3:Terran Conflict the latest (Original IP, semi-newtonian)
Of those, the X series has the biggest fleet battles, but also has as small fights as 1v1. Starshatter is right behind that in scope, with X-Wing in the middle. I've found Her is exclusively fighter vs fighter battles, with about a dozen ships in a big fight.
Capital Ship wise, the market is sadly undersaturated:
-) Starfleet Command Series, SFC 2 being the best, but not the prettiest (Star Trek universe, real-time-turn-based board game adaptation, 2D flight plane, very complex, Isometric View)
-) Starfleet Academy series, Klingon Academy being the latest (Star Trek universe, first person, arcade flight model, rather complex)
-) X series, see above
-) Starshatter, see above
On X, X2 has the best capital ship feeling because you actually were sitting in the captains chair on a fully modelled 3D bridge. Think new Battlestar Galactica CnC sized. Sadly, the rest of the game is inferior to the latter entries in the series.
On SFC2, SFC 1 and 2 are probably the most realistic Star Trek every written - it contains seeking missile weaponry, point defense grids, mines, fighter craft and the everyday beurocracy of a Navy (refits, shipyard capacity issues, wrecking your empires budget by trying to build the biggest Dreadnaught, etc.). Which is probably the reason it is not considered canon.
I'm not going to list RTS/RTT games since, those are a more established genre, and you get a lot of space based ones.
PS.: Don't judge the X-series story by what you get presented in the games - it's an incredibly butchered version of the novelized story (which was actually written first by one of the games developers). Part of the butchering was done to make it playable to more than utter hardcore (lightspeed lag in comms and visuals, time dilation do not a fun game make), part of the butchering was done because of budget problems, and the most horrendous voice actors on the planet chosen by the publisher.