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.|
That is not many!
Explanation: The small, northern constellation Triangulum harbors this magnificent face-on spiral galaxy, M33. Its popular names include the Pinwheel Galaxy or just the Triangulum Galaxy. M33 is over 50,000 light-years in diameter, third largest in the Local Group of galaxies after the Andromeda Galaxy (M31), and our own Milky Way. About 3 million light-years from the Milky Way, M33 is itself thought to be a satellite of the Andromeda Galaxy and astronomers in these two galaxies would likely have spectacular views of each other's grand spiral star systems. As for the view from planet Earth, this sharp composite image, a 25 panel mosaic, nicely shows off M33's blue star clusters and pinkish star forming regions that trace the galaxy's loosely wound spiral arms. In fact, the cavernous NGC 604 is the brightest star forming region, seen here at about the 1 o'clock position from the galaxy center. Like M31, M33's population of well-measured variable stars have helped make this nearby spiral a cosmic yardstick forestablishing the distance scale of the Universe.
Explanation: NGC 253 is not only one of the brightest spiral galaxies visible, it is also one of the dustiest. Discovered in 1783 by Caroline Herschel in the constellation of Sculptor, NGC 253 lies only about ten million light-years distant. NGC 253 is the largest member of the Sculptor Group of Galaxies, the nearest group to our own Local Group of Galaxies. The dense dark dust accompanies a high star formation rate, giving NGC 253 the designation of starburst galaxy. Visible in the above photograph is the active central nucleus, also known to be a bright source of X-rays and gamma rays.
Explanation: Featured in this sharp telescopic image, globular star cluster Omega Centauri (NGC 5139) is some 15,000 light-years away. Some 150 light-years in diameter, the cluster is packed with about 10 million stars much older than the Sun. Omega Cenis the largest of 200 or so known globular clusters that roam the halo of our Milky Way galaxy. Though most star clusters consist of stars with the same age and composition, the enigmatic Omega Cen exhibits the presence of different stellar populations with a spread of ages and chemical abundances. In fact, Omega Cen may be the remnant core of a small galaxy merging with the Milky Way.