Off hand the only two games I can think of are Torch ships http://spacesimcentral.com/ssc/topic/2740-torchships-real-3-d-space-combat/ and http://spacesimcentral.com/ssc/topic/2594-rogue-system/

Both are still being worked on although Torch ships has mentioned an early access version which may be out this month?.

Something you should keep in mind about orbital mechanics:

Most orbits (in circumstances you're likely to encounter in games) take place over periods of days or more.  While in orbit you are in a locally inertial frame, so the physics looks just like it does in games like Frontier or Independence War.  In Star Citizen for example, if you play a swarm match, it usually only lasts half an hour or so, so even though realistic orbital mechanics are not implemented in the game, it's irrelevant because the match doesn't last long enough.  The only time orbital mechanics really matter is if you are playing continuously for a very long period of time, or if you are travelling very large distances without warping (or using some other made-up propulsion system).  

I suppose my point is that there is in fact a very good reason why so few games have realistic orbital mechanics and that games that don't have it aren't necessarily very "unrealistic".  It's simply not the same situation as whether or not a game has what is normally called "Newtonian" (by which I mean locally inertial) physics.  You can in fact have games which seem very realistic, but do not actually simulate orbital dynamics at all.

That said, I look forward to there being a few more.  It was sounding like maybe Elite would be very realistic, but what we got is something that doesn't even feel remotely like a spaceship (sigh).  On the other hand, the orbital dynamics of astronomical objects in that game looks quite convincing.

The FOSS Pioneer has orbital mechanics. We lack the in-depth UI for most operations, and there are no external docking, but you can sure do Hohmann transfers, if you are willing to eyeball it a bit.

Basic orbit display for all bodies and ships are there, with apsis indication too. There's also a rudimentary maneuver planner, which shows the trajectory from your current point in orbit. Also there's a time fast-forward/rewind function for the map, so you can check your position in the future for example.

Docking is quite simplified, the stations just puts you on rails when you enter the gate.

The ships are powerful enough that you are mostly doing brachistochrone transfers. For some ships, you can churn out 20k km/sec deltaVs is you stock up on propellant. And you can have quite a drop in acceleration and turn rate if you fill up a larger ship to it's chin.