Planets outside of our solar system are called exoplanets. As Nike says, we have only spotted 778 so far. We spot planets by watching stars for evidence of a ‘wobble’. As a planet orbits it’s parent star, it’s gravitational pull tugs on the star and causes it to wobble slightly. We can also watch to see if the planet crosses in front of the star (from where we are looking) and causes a brief decrease in the amount of light that it produces.
Estimates of the frequency of systems strongly suggest that more than 50% of Sun-like stars harbor at least one planet. In a 2012 study, each star of the 100 billion or so in our Milky Way galaxy is estimated to host “on average … at least 1.6 planets”. Accordingly, at least 160 billion star-bound planets may exist in the Milky Way Galaxy alone! This is not counting planets in other galaxies spread throughout the universe. If you want to find out more, especially about what the planets might be like (rocky earths or gaseous Jupiters) then check out this website.