Is it possible something in the universe is not orbiting anything? I thought I heard that astronomical bodies could be ejected from a galaxy. If a body was ejected from a galaxy, could it have been ejected faster than the escape velocity of the galaxy? If that is possible would such an object, at least for a period of time, not be orbiting anything?
 A: What Cleonis says is true (+1). But to a degree, it depends on what you mean by something and anything. There are layers of structure in the universe. On a small scale, one object may orbit another. A collection of medium scale structures mutually orbit each other. Larger scale structures do not orbit.
The layers look something like this. You can see a larger version in various Wikipedia articles, such as Local Group or Virgo Supercluster.


Starting "small", the moon orbits the earth. The diameter of the Earth is $12,700$ km. The moon is $3500$ km. The distance between them is abut $380,000$ km, about $30$ times the diameter of Earth.
This is much closer together than the next nearest significant mass, Venus. At its closest, Venus is $38$ million km, $100$ times the Earth-moon distance. The Sun is about $150$ million km away, or about $400$ times the Earth-moon distance. So the Earth and moon are fairly isolated. The moon has a nearly circular orbit around Earth.
Likewise the planets are fairly isolated, and also have nearly circular orbits. The farthest planet is Neptune, about $30$ AU from the sun or about $4$ light-hours.
($1$ AU = $1$ Earth-Sun distance.)

The solar system includes the Oort cloud, a region beyond the orbit of Neptune and Pluto sparsely populated with small icy bodies. It most likely extends from $2000$ to $100,000$ AU. Again, they are fairly isolated from other masses. The nearest star is $4.2$ light years = $265,000$ AU away, and most stars are much farther than that. Oort cloud objects orbit the Sun.
Billions of years ago, the proto solar system contained dust and gas that formed many small objects. Objects like this tend to form circular orbits in a single plane, like the rings of Saturn. They also tend to clump together and form planets, which also have circular orbits in a single plane.
Objects in the Oort cloud were too far away and too sparse to interact with each other enough to circularize their orbits. They are distributed in a sphere around the Sun, and may have highly elliptical orbits.

Beyond this, there are about $100$ billion stars in the galaxy. The galaxy is about $1000$ light years thick and $100,000$ light years in diameter. Starts are about $5$ light years apart on the average. Though they are much closer together in the core of the galaxy, about $0.01$ light year apart.
The stars have largely circular orbits in a plane around a common center, but not nearly to the same degree as in the solar system. Millions have merged into a giant black hole in the center, but this is tiny compared to the galaxy as a whole. The stars do not orbit the black hole. Their orbits are the path caused by the attraction of all the other stars. So they don't really orbit a thing.
Many stars clump together in globular clusters of hundreds to millions of stars. These are sort of like a mini-galaxy inside the galaxy. Except they are not flattened like a galaxy or solar system. They are spherical like the Oort cloud. So a star may orbit inside the cluster as the cluster orbits the galaxy.
There is also the effect of dark matter, which outweighs all of the stars and helps hold the galaxy together. We have not directly seen dark matter. It is just inferred from its effects on the orbits of stars. So we know nothing of its orbit, or even what it is made of.

The next layer is clusters of galaxies.  Typically, the distance to the nearest galaxy is about $20$ galactic diameters. Galaxies are much less isolated than smaller objects.
Galaxies in a cluster orbit each other like stars in a cluster.
In our own local group, there are two giant galaxies, our own and the Andromeda galaxy. Plus about $100$ smaller galaxies. The diameter is about $10$ million light years.

Beyond this, objects predominantly approach each other or fly apart. It is not orbital. Clusters of galaxies form structures like filaments or soap bubbles.
The Virgo Supercluster contains our local group and about $100$ other groups and clusters. It has a diameter of about $110$ million light years.
The Virgo Supercluster is one arm of an even larger group called the Laniakea Supercluster. This contains the Great Attractor, a concentration of galaxies so great that its attraction has a noticeable on the velocity of matter for hundreds of millions of light years around.
On this scale the largest influence is the expansion of the universe. Everything moves away from everything else. Motion is not away from a common center. Rather it is like the separation of dots on a balloon being inflated. Far away object are separating faster than nearby objects. The Great Attactor diminishes this expansion for nearby matter.

On scales larger than this, there is no noticeable structure. Matter is spread fairly uniformly across the observable universe. This continues as far as we can see, more than $10$ billion light years.
A: It is my understanding that such events do occur.
My understanding is that in globular galaxies stellar density is higher than in most galaxies, and thus the gravitational slingshot events that lead do ejection occur comparitively most often in globular galaxies.
Given the distances between galaxies it can take an ejected star billions of years to traverse the space from one galaxy to approching another galaxy.
I expect that in intergalactic space there must be points where the combined gravitational influence of all the surrounding galaxies is such that all contributions drop away against each other. Let me refer to those points as 'equilibrium points'. It seems to me that under those circumstances it is reasonable to regard motion in the vicinity of those points as not-orbiting-anything.
It would require fine-tuning for an object to end up with zero velocity and zero distance with respect to the equilibrium point.
But there is no clear demarcation between is-in-orbit and is-not-in-orbit; it's a judgement call. What if the ejected celestial body is ejected with a velocity such that it takes 10 billion years to return to the galaxy where it was ejected from? For a comparison of astronomical timescale: generally disk-shaped galaxies tend to have a rotation rate of about once every billion years.
The point is: while gravity falls off with the square of distance, there is always some gravity, no matter how large the distance becomes. An object in intergalactic space is never not subject to any gravity. The closest to not-subject-to-gravity is that the combined gravity vectors of the surrounding galaxies add up to zero.


The smallest system that is capable of giving rise to an ejection event is a three body system. (There must also be significant difference in mass.)
In our solar system the planets are sufficiently far apart such that planet-planet interaction is not strong enough to de-stabilize the system.
But if you have a system with a primary, a secondary and a tertiary, then in order to be long term stable the tertiary must be either very close to the secondary, such as in the case of the Moon being close to Earth, or it must be far away, like another planet.
If the primary and secondary are roughly the same mass (and the tertiary having far less mass), then there is no stable orbit for the tertiary. The motion of the tertiary will not be cyclic, and eventially the tertiary will either impact the primary/secondary, or there will happen to be a combination of gravitational slingshots that end in ejecting the tertiary.
When the ratio of masses of the primary and secondary is 25:1 or higher, then for the tertiary there are orbits avaialble that do not end with a collision event, nor with being ejected. Those long term orbits are referted to as 'Lagrange point' orbit. The Lagrange points L4, and L5 have that property.
(The ratio is not exactly 25:1, I'm rounding to an integer)
