Re: How Far Can You See At Night?

This question appears to be asking two different things. It is difficult 
to answer because faintest and farthest are different concepts. We see 
the stars at night based totally on the amount of light that reaches us
from that star. Some of the objects that we can see are not stars but
entire galaxies of stars. The light from a galaxy or cluster of stars would 
be brighter than a single star at the same distance. For example, Rigel 
is many times brighter than Alpha Centauri which is much closer. Another
major factor that needs to be considered is the viewing conditions. In a 
city fewer objects will be visible. In the rural areas away from light 
pollution, more objects would be visible. 
Now, let us assume that we have very good viewing conditions. The brighter 
the object, the farther away it can be for us to still see it. 
As for stars, Sirius is the brightest in the Northern sky. It is 2.7 parsecs
away (a parsec is about 3.26 light years, a light year is about 6 trillion
miles). Antares, in Scorpio is 120 parsecs away. Deneb, in Cygnus is 
430 parsecs away. All of these are very visible in the Northern sky even
under less than ideal conditions. The Andromeda Galaxy is visible under
good conditions and it is much larger than our own galaxy. It is a distance 
of 675000 parsecs away. Other galaxies that we can see with our eyes can
be still farther. 
We use the magnitude scale to determine brightness of objects. A jump of 
1.0 is 2.5 times the brightness. A jump of 2.0 is 2.5 times 2.5 the 
brightness. 2000 years ago an astronomer named Hipparchus grouped all 
the stars by brightness. The brightest were "first magnitude, the next 
brighest were "second magnitude and so on. The brightest object we can 
see is about magnitude 6. So by looking at a star chart you can determine
which objects you should be able to see. 
This link is to a catalog of the Messier objects. Many of these are visible
with the naked eye.
The Messier Catalog of Objects
There several references that can give you the magnitude and distances of
many stellar objects. Any good star atlas can. In the Northern Hemisphere
the farthest object that I can personally view with the naked eye under
ideal condtitions is probably the Andromeda Galaxy, at a distance of 
2.2 million light years.