There are surprisingly few. And it's not been yet a century that we've known there were any other galaxies.
This is a list of galaxies that are visible to the naked-eye, for at the very least, keen-eyed observers in a very dark-sky environment that is high in altitude, during clear and stable weather.
|Milky Way Galaxy||-26.74 (the Sun)||0||Sagittarius(centre)||This is our galaxy, most things visible to the naked-eye in the sky are part of it, including the Milky Way composing the Zone of Avoidance.|
|Large Magellanic Cloud||0.9||160 kly (50 kpc)||Dorado/Mensa||Visible only from the southern hemisphere. It is also the brightest patch of nebulosity in the sky.|
|Small Magellanic Cloud(NGC292)||2.7||200 kly (60 kpc)||Tucana||Visible only from the southern hemisphere.|
|Andromeda Galaxy (M31, NGC224)||3.4||2.5 Mly (780 kpc)||Andromeda||Once called the Great Andromeda Nebula, it is situated in the Andromeda constellation.|
|Omega Centauri(NGC5139)||3.7||18 kly (5.5 kpc)||Centaurus||Once thought to be a star and later a globular cluster, Omega Centauri was confirmed as having a black hole at its center and thus its status has been changed to being a dwarf galaxy as of April 2010.|
|Triangulum Galaxy (M33, NGC598)||5.7||2.9 Mly (900 kpc)||Triangulum||Being a diffuse object, its visibility is strongly affected by even small amounts of light pollution, ranging from easily visible in direct vision in truly dark skies to a difficult averted vision object in rural/suburban skies.|
|Centaurus A (NGC 5128)||7.8||13.7 ± 0.9 Mly (4.2 ± 0.3 Mpc)||Centaurus||Centaurus A has been spotted with the naked eye by Stephen James O'Meara|
|Bode's Galaxy (M81, NGC3031)||7.89||12 Mly (3.6 Mpc)||Ursa Major||Highly experienced amateur astronomers may be able to see Messier 81 under exceptional observing conditions.|
|Sculptor Galaxy (NGC 253)||8.0||11.4 ± 0.7 Mly (3.5 ± 0.2 Mpc)||Sculptor||According to Brian A. Skiff, the naked-eye visibility of this galaxy is discussed in an old Sky & Telescope letter or note from the late 1960s or early 1970s.|
|Messier 83 (NGC 5236)||8.2||14.7 Mly (4.5 Mpc)||Hydra||M83 has reportedly been seen with the naked eye.|