Well, that depends what you mean by “see”.
As tonbo0422 alluded to, researchers at IBM’s Almaden research center wrote “IBM” using xenon atoms on a nickel surface. You can see an image here: http://www.almaden.ibm.com/vis/stm/images/stm10.jpg
As you might guess, it’s not like that image is a photograph. That image was constructed by gathering data from a STM (scanning tunneling microscope). The atoms were also moved into that shape using the STM, and into many other shapes, as shown in the gallery: http://www.almaden.ibm.com/vis/stm/gallery.html
What we’re seeing in these images are the electromagnetic interactions between the STM “tip” and the atoms, which might seem like a cheat (we’re not really seeing the atoms themselves)… but your eye just uses a different type of electromagnetic interaction with reflected photons to see anything, so it’s close enough.
No, you can’t really see an atom. But there are certain properties about it that are more than a model.
First, forget everything you’ve ever seen about electrons orbiting in rings around the middle (nucleus) of the atom. That model was proven wrong within a few years of its introduction, yet it somehow persists.
An atom is actually composed of a nucleus surrounded by a cloud of electrons. The nucleus is made of protons and neutrons, but it’s probable that they aren’t really divided into individual particles when they’re in the nucleus, so it’s safe to just think of the nucleus as roughly a sphere. The electrons have a wavelength roughly equal to the diameter of the atom–meaning they aren’t really in any particular place (thus the cloud surrounding the nucleus, even if there’s only a single electron, such as in a hydrogen atom).
BTW, the reason you’re visible is that electrons are able to absorb certain photons, while other photons are reflected (either by “bouncing off” of the nucleus, or by being absorbed and re-emitted by the electrons). Different atoms (and arrangements thereof) have electrons that absorb different wavelengths (colors) of photon, resulting in different colors of photons being reflected to be picked up by your eye.