When it comes to seeing faint things, our eyes aren't that bad. Yes, some other animals use tricks to be able to see fainter things than we can (like reflective linings to the eyes, or more sensitive rods in the eyeball). But, given time to adjust to the dark, our eyes can see stars when only a dozen or so photons of light are hitting our eyeball every second. That's not too bad! So, how far our unaided see?
On a clear, moonless night, most people with decent vision can see the Andromeda Galaxy (Messier 31), and under excellent conditions, many people have been able to pick out the Pinwheel Galaxy (Messier 33, a.k.a. the Triangulum Galaxy. Andromeda is about 2 million light-years away, and the Triangulum Galaxy may be 3 million light-years away.
This sounds really far, but, in astronomical terms, they are neighbor galaxies. Andromeda, Triangulum, and the Milky Way galaxies are all part of the "Local Group" of galaxies. The Local Group is kind of like a solar system of galaxies. All the galaxies in the Local Group are bound by gravity and are very slowly orbiting one another. In a few billion years, we may even collide with the Andromeda Galaxy.
Some eagle-eyed people looking on pristine nights from mountain-top sites have been able to see Messier 81, a galaxy about 12 million light-years away. Messier 81 is not part of the Local Group of galaxies, but is instead the heavyweight core of the closest group of galaxies outside our own. But this is a little like being able to see the house across the street in a large metropolis -- not too impressive. The most distant galaxies the Hubble Space Telescope can see are a thousand times further away than Messier 81.
However, last Wednesday morning, March 19, 2008, humans had a chance to see an event with their own eye that was seven billion light-years away, or halfway across the visible Universe. At 6:12am and 49 seconds Universal Time (2:12 am Eastern Daylight Time), the Swift gamma-ray satellite detected a burst of gamma rays coming from the direction of the constellation Bootes (near the Big Dipper). Robotic telescopes on the ground instantly moved to this portion of the sky, where they found a point that brightened from invisibility to magnitude 5.5 in only 20 seconds. It stayed bright for about 30 seconds, and then started to fade away to the nothing from which it came.
For those who don't speak magnitudes, a magnitude of 5.5 is bright enough for the human eye to see on a drak, clear night, but just barely. Later analysis determined that the light these robotic telescopes saw came from a galaxy nearly 7 billion light-years away.
The short of the story is that, had you been lucky enough to have been outside, had your eyes adapted to the darkness, and knew where to look, you would have been able to see a faint spot of light coming from a galaxy halfway across the visible Universe last Wednesday morning, but only for about 30 seconds. As far as we know, no human knowingly saw this event -- the "flash" was too faint to notice unless you knew right where to look, and the 30 second time interval was not long enough for anyone to have been able to learn about the gamma ray burst, consult their star charts, look, and be certain what they were seeing.
Still, it is exciting to think that, in some circumstances, it might be possible for a human with no equipment other than their eyeball to see something that far away. Gamma ray bursts happen about once a day, and while this is the first burst to have gotten this bright, a flash like this probably happens every few years. We've just never had the technology before. Maybe some day in the next decade or two, someone will get lucky enough to catch a few photons from en explosion that happened billions of years ago with nothing but their eye.