There are about 80-100 billion galaxies in the observable universe, that is, that part of the universe visible to us. There may be more in that part of the Universe beyond our observable limit, which occurs about 400,000 years after the Big Bang. Before that time, the universe remains opaque to us. It’s like trying to see through a dense fog. After this time, the “fog” lifted and light could traverse the universe. This occurred because the universe expanded and cooled, allowing electrons to pair with protons and light to travel without bumping into the free electrons.
This is a difficult number to know for certain, since we can only see a fraction of the Universe, even with our most powerful instruments. The most current estimates guess that there are 100 to 200 billion galaxies in the Universe, each of which has hundreds of billions of stars. A recent German supercomputer simulation put that number even higher: 500 billion. In other words, there could be a galaxy out there for every star in the Milky Way.
Most of the galaxies in the Universe are probably tiny dwarf galaxies. For example, in our Local Group of galaxies there are only 3 large spiral galaxies: the Milky Way, Andromeda, and the Triangulum Galaxy. The rest are dwarf and irregular galaxies.