That can change with the different seasons, but this time of the year it would be the Andromeda Galaxy, some 2 million light years distant. It lies, for lack of a better description, straight up and is only a faint smudge of light. It's a spiral arm galaxy, not unlike our own Milky Way...
Its all down to magnitudes of stars or galaxies. The human eye can see anything of magnitude 6 or less. As a guide a full moon is minus 12 so easily visible. The Andromeda Galaxy has a magnitude of 4.5 so it is visible and is faint but there will be fainter objects visible. Pluto has a magnitude of 7.8 so is just out of view but the furthest i can find is 61 Cyg B with a magnitude of 6.03 might be just visible with good eyesight. Thats a mere 11.1 million light years away.
Thanks for your answers (even yours mimififi ho ho groan ;o)
Actually I saw the andromeda galaxy (just the faintest smudge) the night before I posted, but I wasn't aware this was the furthest thing I could see with my indecent eyes.