Is it not impossible to see a single atom using visible light? We see things because some light gets bounced off them, and this "bounced" light is due to electrons jumping from higher energy states to lower energy states. So is it really possible to see a single atom using visible light?
 A: 
We see things because some light gets bounced off them, and this "bounced" light is due to electrons jumping from higher energy states to lower energy states.

That is not the way we "see" things. Photons getting  absorbed and re-emitted is not the most probable interaction of photons with atoms, particularly of visible light. Photons interact with the electric and magnetic fields of atoms (collectively) and scatter elastically, thus not changing frequency/color, most of the time. Excitation and re-emission can happen if the atom in question has energy levels at that frequency of visible light, and is called fluorescence . Usually this is not so, and the photons hitting a surface made up of atoms reflect the shape of the solid and we "see" when some of those photons fall in our eyes.

So is it really possible to see a single atom using visible light?

Now for single atoms and visible light this is not possible 

No one has ever seen an atom. The wavelength of visible light is more than 1000 times bigger than an atom, so light can not be used to see an atom.

There are different ways of "seeing" other than with visible light, using interactions of atoms and mathematical models this has been done, like blind people with touch:

Scanning Tunneling Microscopes work by moving a probe tip over a surface we want to image. The probe tip is an extremely sharp - just one or two atoms at its point. There is a small electric voltage on the probe tip and depending on the height of different parts of the surface, more or less current will flow from the tip to the surface. By noting the changes in current we can recreate an image of the surface at the atomic level.

They have "seen"  a single hydrogen atom

Physicists in the US claim to have used a transmission electron microscope (TEM) to see a single hydrogen atom – the first time that a TEM has been used to image such a light atom. The breakthrough was made by supporting the atom on graphene — a sheet of carbon just one atom thick. The team has also been able to watch hydrocarbon chains move across the graphene surface, suggesting that the technique could be used to study the dynamics of biological molecules. 

Edit after comment.
Another way of seeing is in using fluorescence of molecules , as in fluorescence microscopes.

The specimen is illuminated with light of a specific wavelength (or wavelengths) which is absorbed by the fluorophores, causing them to emit light of longer wavelengths (i.e., of a different color than the absorbed light). The illumination light is separated from the much weaker emitted fluorescence through the use of a spectral emission filter. Typical components of a fluorescence microscope are a light source (xenon arc lamp or mercury-vapor lamp are common; more advanced forms are high-power LEDs and lasers), the excitation filter, the dichroic mirror (or dichroic beamsplitter), and the emission filter (see figure below). The filters and the dichroic are chosen to match the spectral excitation and emission characteristics of the fluorophore used to label the specimen.2 In this manner, the distribution of a single fluorophore (color) is imaged at a time. Multi-color images of several types of fluorophores must be composed by combining several single-color images.

They have seen single molecules with this method.
Update 2018, thanks to comment by Mr.WorshipMe

A single atom is visible to the naked eye in this stunning photo

...

Two metal electrodes, two millimetres apart, held the strontium almost motionless in a strong electric field as it was illuminated with a blue-violet-coloured laser.

Note that the atom is visible in the photo to the naked eye , not looking at the gap directly, where the atom is suspended. This is the simplest proxy method at the moment of getting a signal of a single atom, with visible light. 
BTW the article propagates the misinformation that we see by light absorbed and re-emitted. We see by light scattered elastically off the objects. Absorbed and re-emitted light looses phase correlations, and the reflected image  would be lost; in the case of absorption and re-emission one has fluorescence .
Strontium has fluorescence spectra, ( google search gives a number of references) so further study would be necessary to determine whether the spot registered on the film is fluorescence or reflection.
A: It is possible to set up experimental conditions which allow you to take a ordinary photograph of a single atom in visible light.
This works by building an electromagnetic trap (in particular a magneto-optical trap); getting some atoms in there; shaking them gentle to boil atoms away until only one remains; then exciting it to fluoresce. The linked article by the University of Otago atomic physics group does not seem to claim that sufficient intensity can be achieved to make the atom visible to the unaided eye, but you should be able to image it using off-the-shelf equipment.
Their initial paper may be Andrew J. Hilliard, Matthew McGovern, Tzahi Grünzweig, and Mikkel F. Andersen, "Consistent isolation and fluorescence imaging of individual atoms", Imaging and Microscopy, 13, 32-34 (May 2011) , but they list several related papers.
A: If you mean that you want to observe some physical material using only visible light (e.g. through an insanely well-crafted light microscope), and discern where the invividual atoms in the material are, then no, I don't believe that it is possible.
The reason  is that you can usually only see objects that are roughly as small as the wavelength of the light you use. Since visible light consists of photons with wavelengths in the range 400-800 nm, this means that you can only see objects down to a minimum of 400 nm in size. However, the distances between atoms in a material are typically in the range 0.1-0.3 nm, which is 1000 times less than this. Thus, the conclusion is that you can't see the atomic structure of e.g. a crystal by using only visible light.
However, you can observe such small structures using other particles. More specifically, you can produce photons with a 0.1 nm wavelength, which falls under the category of X-rays, or you can also produce electron rays with such wavelengths; and both of these approaches are commonly used in e.g. diffraction experiments to take pictures of the crystal structures of various materials.
