Supermassive Blackholes

The UCLA Galactic Center Group actually has real-time data of stars orbiting the SMBH in our galaxy.

See: http://www.astro.ucla.edu/~ghezgroup/gc/pictures/orbitsMovie.shtml

 

From a more theoretical perspective, when you are far enough away from a black hole, you cannot tell the difference between it and a normal star. So for all intents and purposes, large orbits around black holes are the same as orbits around any other body. You can have circular, or elliptical orbits just as with any other body. Things get strange as you get closer to the hole though, with things like unstable circular orbits and zones where you cannot orbit at all. But I think the vast majority of stellar objects in orbit around SMBHs do not fall into these categories.

 

As Nabeshin mentioned when far enough away from the SMBH event horizon things will go unnoticed due to the amount of mass the star once had isn't changing, it is just getting condensed according to the Schwarzschild radius. In fact our orbital velocity would not change if the Sun became a black hole. Now as an object gets closer and closer to the event horizon their orbit will change dramatically, turning quite chaotic. The only difference between a quiet SMBH (within our own Milky Way) and an active SMBH (like the one in M87) is that all of the stars which were close enough or inside the event horizon have been sucked in, leaving stars that were far enough away, untouched. Other than that they are pretty much the same.