If you have a dark site, and you know where to look, you can see the Andromeda Galaxy with the naked eye. IIRC, that is about 2.5 million light years away, and is generally considered to be the most distant object visible without optical aid. However, some people have seen more distant galaxies from extremely dark sites.

Those in the southern hemisphere can easily see the Megallanic Clouds, which are dwarf galaxies that are much closer to the Milky Way than Andromeda is.