Because of how they work, it makes more sense to talk about a telescope's light gathering ability and angular resolution than how far it can see. If you're including a specific detector (your eyes, some CCD, whatever), you can also directly talk about the faintest objects possible.
There is no limit to how far you can see, if the object is bright enough.
Your eyes can see individual stars that are up to 16,000 lightyears away. You can also see the diffuse glow of the galactic core, which is around 25,000 lightyears away. And on a dark night you can even spot the glow of the Andromeda galaxy, which is 2,500,000 lightyears away.
A telescope doesn't change how far you can see; it changes how faint of an object you can see. An object that is twice as far away has to be four times as bright for you to be able to see it. An object that is 10 times as far away has to be 100 times as bright for you to be able to see it. Telescopes collect light from a large area and focus it into a smaller area, allowing you to see objects that would ordinarily be too dim.
With a big enough aperture and enough time you could see the surface of the nearest exoplanets. But that would require something with an aperture the size of the moon or jupiter.
What kind of resolution are you looking for? How many times magnification? You can see things more than a light year away now. You can see the Andromeda Galaxy with the naked eye and that's millions of light years away.
ElevationAV t1_j3z6vgq wrote
you can see stars without a telescope, they are more than 1 light year away