Further than you might think, is the answer. It isn’t exactly clear where the cut-off is, but it’s certainly more than 3 million light-years out.
We know this because of galaxies. Galaxies … the Universe is full of them, but which can you see?
Well, straight off, you can see our own. Look up on a dark, clear night and you’ll see a murky, silvery blur running across the sky. This is the Milky Way. You see it as a fat line because our Sun orbits close to the plane of the galactic disk, and thus you’re looking straight into the ‘fat’ bit.
What about further afield?
Well, the next most obvious ones are the Small and Large Magellanic Clouds. They’re so-called because the first Western explorer to report seeing them was the Portugese navigator Magellan, in the 16th Century. The Clouds, sadly, are southern-hemisphere objects, and quite invisible from the northern hemisphere. What they are is two so-called ‘dwarf’ galaxies, and in fact they are in orbit around ours. Effectively they are ‘moons’ to our galaxy. They’re also much smaller – both are less than 15,000 LY across, compared to ~100,000 for our own galaxy. They also contain rather fewer stars – the total mass of the so-called Large Magellanic Cloud, for instance, is about 1/10th that of our galaxy. The Small Magellanic Cloud contains only a few hundred million stars, compared to ~100 billion for our galaxy.
The two clouds are magnitude 0.9 and magnitude 2.7 respectively, making them rather bright relative to other galaxies.
The next object should be the Sagittarius Dwarf Galaxy. However it’s relatively faint, with a magnitude of 4.5. Also, there’s some discussion about whether it still counts as an independent galaxy – you see, ours is currently eating it. It orbits close to the Milky Way – in fact, its orbit actually takes it through the stellar disk of our galaxy. And every time it passes through its voracious neighbour, it loses some stars to us. (In fact, on occasion, entire globular clusters have been accreted from our unfortunate neighbour.) The Sagittarius Dwarf was only discovered as recently as 1994 – paradoxically its close location makes it hard to resolve from the galactic stellar background. (‘Is that blob a galaxy or ‘just’ a halo stream?’)
Moving away from the Sagittarius Dwarf, we come to the Andromeda Spiral.
Andromeda is an easy case. It’s the next big galaxy in the Local Group. In fact, it’s bigger than ours. Andromeda is located at a distance of 2.2 million LY (or thereabouts). Recent estimates by the Spitzer Space Telescope suggest that it contains around 1 trillion – 1,000 billion – stars, as opposed to perhaps 200 billion for our galaxy. Oddly, though, it’s not actually that much more massive. Mass estimates range between 20% heavier than our galaxy to about it being about equal mass-wise. (Presumably this implies that Andromeda is preferentially forming smaller, lower-mass stars, although why that might be escapes me.) Andromeda is reasonably bright, with a visual magnitude of about 3.4ish. You can see it from any dark-sky sight, as a faint thumb-sized smudge in the sky. (What you’re seeing is actually the galaxy’s core. The entire thing would be six times bigger than the full Moon, but the disk itself is too faint for us to see, sadly.) The Andromeda Spiral is old knowledge – recorded observations go back to the year 964, and it will certainly have been seen long before that.
(A brief aside at this point: The galaxies preceding this point are the only ones in the sky to show blue shifts. They’re moving towards us, not away. In the case of the Clouds, this is just orbital motion. In the case of Andromeda, it may actually be on collision course, dependant on radial velocity. If it does pay us a visit, though, it won’t be for another billion or so years, and by then solar expansion will have made the Earth uninhabitable, so this is Not Our Problem.)
Moving beyond Andromeda, things get hazy.
There are plenty of galaxies out there, but millions of light-years is a long way, and the light is very dispersed by the time it reaches us. The human eye gives up somewhere around magnitude 6 in most people, but it is possible sometimes to see things that are fainter. These require two things; exceptionally dark skies and exceptionally-good seeing conditions.
Beyond Andromeda, the next object that can sometimes be seen is the Triangulum Spiral. The Spiral of Triangulum is another spiral galaxy, like ours and Andromeda. It’s one of the ‘big three’ that dominate the Local Group. It’s currently around 3.3 million LY away from us. It’s rather smaller than both us and Andromeda – current estimates suggest about 40 billion stars. Triangulum has a magnitude of 5.72, which is getting a bit marginal. Although that is technically within reach, any cloud cover or sky glow will quickly obscure it. For this reason, Triangulum is sometimes used as a test of sky conditions. (If you can see Triangulum, then conditions are good!)
Now I’ve mentioned +6 magnitude as a hard limit. This is a bit deceptive. If you can combine moderate altitude with great, great distance from brightly-lit urban areas, then in fact the eye can just about scrape up to magnitude 8. (This is more impressive than it sounds – each magnitude interval is ~2.5 times fainter than the one before it, so mag 8 is actually 6.25 times fainter than mag 6.)
There are a few objects sat on this borderline. Bode’s Galaxy – another spiral, this time at 11.8 million LY – presents a magnitude of 6.94, and some people have claimed to see it. Also there are claims for Centaurus A, at magnitude 6.84. Centaurus A is a particularly-interesting object, as it’s believed to be the origin of some cosmic rays. There is also a claim for the Sculptor Galaxy, although I have to say I’m not sure I believe it. Magnitude 8.0 is very faint. I think it’s fair to say that this object will only be a possibility for people with near-perfect eyesight, under near-perfect conditions. (Sadly, that rules me out.)
But nonetheless, one thing is clear. The human eyeball can receive and respond to light from millions of light-years away. Given that the eyeball evolved here on Earth, and presumably never ‘needed’ to see beyond the next valley, I think this is pretty damn amazing.