In air, when there is light propagating in a direction, we can still see it even when it is not primarily travelling in our direction, because a small part of the light hits the air molecules, and changes its direction; it travels towards us.
Does this mean that, in a vacuum, you would not be able to see light which is not travelling towards you?
If the light has nothing to scatter off of to reach your eyes you won't see anything.
No. Light has to physically interact with the sensors in your eyes for you to be able to see it, and likewise for cameras, too.
The reason you can see "light beams" in a terrestrial environment is that in the atmosphere, some of the light can be scattered so it does get into your eyes. In vacuum, this does not happen.
In a perfect vacuum, not only can you not see light that isn't traveling toward you, you can't even see light that is traveling toward you until it actually reaches your eyes.
Light must reach your eyes/detectors one way or another - no matter vacuum or not. It may be directed there in the first place or scattered somehow.
Then again, scattering is a complex matter.
Both your eyes and the light source have some edge diffraction so SOME light will get into your eyes (given enough time to propagate) no matter where everything is directed. If the source is strong enough and the eyes sensitive enough, you will see something.
"Vacuum" is relative, too. Even the intergalactic space has some atoms flying around. There is also a cosmic microwave background, so you can expect some photon-photon scattering (really hard to observe, but has rather strong theory backing it).
You can only see light that arrives at your eye, whether in a vacuum or not. In air, when you 'see' sunbeams, for example, you are actually seeing light that has been scattered from the sunbeam towards your eye. In a perfect vacuum there would be nothing to scatter light, so you would see only light that has travelled directly to you from its source.
Thinking through this by attempting to distill it to its essence.
"Seeing light" is another way of saying, "photons are striking my eye." That is, in order to see light, photons must strike my retina.
Now, consider a single photon within the beam. In order for my eye to detect it, the photon must change direction and strike my retina.
This could happen if there's matter for the photon to bounce off of. But, in this case, it's traveling through a vacuum, so there is no matter, and the photon will never strike my retina.
Perhaps there's one way this could happen - if the photon passes through a mass' gravity well, veering toward my retina. There could hypothetically be a vacuum surrounding the mass, but in practice the vacuum won't be perfect. But of course, at that point the light is now traveling toward my eye.
So, the answer is "no." Light consists of photons, a photon must strike my eye to be seen, and a photon that strikes my eye is light traveling toward my eye.
In a universe that is shaped like the three-dimensional surface of a basketball whose space would be expanding at a rate initially almost exponential but eventually only quasi-inertial, like each of the local universes in at least one "bouncing" and inflationary cosmology (Nikodem J. Poplawski's "cosmology with torsion", described in numerous papers written between 2010 and 2020 that are available free on Arxiv), photons would (since they each have an infinitesimal relativistic mass) be orbiting through the curvature of the aforementioned surface's volume, so that you would eventually be able to see even light that had been emitted from the curved region to your rear, if you'd somehow wait (and survive) long enough after having somehow made an appearance on the scene.
However, regarding a question (at https://astronomy.stackexchange.com/questions/19013/statistical-techniques-for-estimating-distribution-of-mass) on the Astronomy Stack Exchange, Pela's answer describing the most standard procedure for estimating mass distributions shows a disproportionately large distribution of mass in the brightest and most red-shifted clusters of galaxies, which suggests that the probability that any photon you might see would not have been involved in one or more refractions might be very low.
As the other answers state, the answer is no, if there is nothing for light to scatter off of, to change its direction towards you, you will not see anything.
I would like to add, that it might be interesting to consider two things:
There is no perfect vacuum, and the real vacuum in our universe does have certain particles, some of which might scatter light towards you.
Does vacuum (empty space) exist?
Curvature (extreme) can exist even in vacuum. You might be surprised to realize that light that originally seems in 3D space to not be moving towards you initially, might end up actually moving towards you because of spacetime curvature. Examples are gravitational lensing, or photons orbiting black holes (like the photon sphere).
