Frontier: Elite 2 and
Frontier: First Encounters (get JJFFE/D3DFFE with the last one as it was originally pushed out of the door by greedy suits in something resembling late alpha stage) are old games (1993 and 1995 respectively), but probably your best bet, unless you want something hardcore, but not much of a game - like Orbiter.
Both Frontiers feature Newtonian in-system flight mechanics, full scale, approximately astrophysically correct planetary systems with simulated orbital motion, planetary rotation (inducing day-night cycles and Coriolis' Force), seamless planetary landings, relative frames of reference and gravity (somewhat simplified, as it seems to only account for dominant source of gravity per object, but you can still slingshot and orbit).
Gameplay is sandbox in nature, allowing you to do anything you damn please (as long as you can afford it) and doesn't include any sort of end condition aside from death/imprisonment (FFE includes handcoded plotline, but it can get completed by NPCs if you don't pay attention), the gameworld is procedurally generated (save for our solar system, and quite a few well known or nearby stars) and encompasses entire galaxy, though, admittedly, slightly downscaled (to about half billion systems) and flattened.
The variety of careers includes courier, passenger transport, military, planetary mining, asteroid mining, piracy, bounty hunting, assasination, hydrogen scooping and trading. There are multiple ship types and upgrades available, cargo and individual ship systems (including individual directional thrusters) can get destroyed/damaged in a fight, collision, or due to lack of maintenance. Some cargo doesn't tolerate vacuum, live cargo also requires life support. Some types of cargo are illegal in certain systems though can fetch nice prices on black market.
You travel between the systems using hyperdrive that can be activated at any time provided you have fuel, are at least 12km above nearest planetary surface and not too close to orbital station's entry corridor. Hyperdrive can then take you to any system within range (several to tens of ly, usually), with exit point being random (but time and location dependent - useful in pursuits) point approximately 10AU from target system's centre. Then it gets Newtonian.
Thankfully the game has up to 10000x time compression.
Graphics has obviously aged a lot (hello? 286, Amiga, Atari ST), but it aged surprisingly well - the game uses extensive amount of Bezier curves, curvy polygons, a lot of detail, powerful LOD algorithms and coloured lighting. FFE looks better overall, but has lost some distinct elements, like nifty, Bezier based clouds over planets with atmospheres.
http://www.youtube.com/watch?v=rc-0rf1J ... re=related <- a vid showcasing French version of FE2 (it's badly compressed, though, the guy doesn't know how to fight properly and "jousts" with semi-auto engines flinging him around out of control and the soundtrack is obviously not the in-game one).
There is also Pioneer - open source, fan-made remake of Frontier currently somewhere in playable alpha stages. It looks very promising.
I wouldn't bother with original Elite, as it's not Newtonian but features incredibly simplistic arcade'y flight model instead. It started the genre, but has been since surpassed in all possible ways and thus serves mostly as historical curiosity.
I-War series - I've only played I-War 2 but would rate it much lower than Frontier. It's a good game, and handling your ship feels nicer than in Frontier (due to rotational inertia), but the interface is an absolute clusterfuck, backgrounds don't resemble space and are inconsistent with each other, there are no planetary landings, no gravity, no orbital motion, interplanetary drive kills the sense of space (and is inconsistent with description), AI (and often mission designers) fails to understand Newtonian in a very exploitable fashion, and stealth mechanics is inconsistent with perception (and the fact that there is no stealth in space
). There is also the fact that there is no permanent hull and subsystem damage, as everything gets autorepaired at speed resembling regen in modern popamoles. It also has the most retarded laser ever conceived, far surpassing the inevitable idiocy of beams being visible in space - it has beam slowly extend to its maximum length - no joking. Thankfully beam weaponry plays marginal role in game, eclipsed by all types of energy projectiles and missile weapons.
Still, it has a lot of nifty stuff like sub-targeting, good fluff, good piracy, good trading, a lot of missiles and equipment, remote control interface, the best shield system in existence and is a fun game overall.
Darklight Conflict - I honestly don't know why it was mentioned here as it's an arcade'y shooter through and through, with typical arcade'y plot, arcade'y flight and so on. Not in the least bit realistic.
Still, despite arcade'y flight mechanics, it does use inertia quite a lot, and apart from unnatural constraints, its physics can be fun and feel as if someone took a decent Newtonian system and stuffed it between arcade'y limits. Bastard.
Nexus: The Jupiter Incident is not a spacesim (is a tactical fleet sim) and is not Newtonian. IT does, however use Newtonian stylistics prominently (retros, directional thrusters and so on), and feels very space-like. A good game overall, but very imbalanced, don't play on high difficulty settings. Also, devs couldn't into aliens - results are embarrassing.