The small and large Magellanic clouds are galaxies that are orbiting our own galaxy. How many such "galactic satellites" do we know of?
Wikipedia's Local Group lists the following items as galaxies, dwarf galaxies, or possibly galaxies. You should refer back to the Wikipedia page, but here is a summary:
Galaxies: Sagittarius Dwarf Galaxy, Large Magellanic Cloud, Small Magellanic Cloud
Dwarf Galaxies: Ursa Minor, Draco, Carina, Sextans, Sculptor, Fornax, Leo I, Leo II, Ursa Major I, Ursa Major II
Disputed Dwarf Galaxy: Canis Major
other: several additional ultra-faint dwarf spheroidal galaxies
However: There is a much longer list of "galaxies" (over 60 items) Wikipedia's Satellite galaxies of the Milky Way
Hopefully another answer will be posted discussing just how galactic these need to be to be called galaxies, and if they are all known to be gravitationally bound to the Milky Way or just in its proximity.
Table 2 from Drlica-Wagner et al., 2020 contains a list of 61 confirmed and candidate Milky Way satellites. Two of these are unconfirmed, and two are probable star clusters. 39 are confirmed satellite galaxies with known kinematics and 18 are probable satellite galaxies. These are all in a radius of about 300 kpc from the Sun.
Deeper surveys in the coming years will possibly find another 150 satellites, since Nadler et al., 2020 finds that there are likely $220\pm 50$ satellite galaxies of the Milky Way.