Billions and billions, according to Dr Carl Sagan.

The number of stars varies enormously between galaxies, so it's not really possible to state how many are in any given galaxy with any real meaning - for example, a giant elliptical galaxy might have 999,900,000,000 more stars than a dwarf galaxy.

Our galaxy, the Milky Way, is believed to have around 300 billion stars. A dwarf galaxy might have as "few" as 100 million, whereas a giant elliptical galaxy might have 100 trillion and be 700,000 light years across.

It's thought that there are approximately 70 billion trillion stars in the observable universe (ie that part close enough for light and electromagnetic radiation emanating from it to have reached us in the time since the sources came into being), divided between 2 trillion galaxies. If you named an equal number of galaxies in the observable universe after every living person on Earth, we'd each have 263 galaxies named after us. If you did the same with the stars, we'd all have 9 trillion named after us.