Number of stars & planets in Milky Way Galaxy?

A consensus number is that there roughly $10^{11}$ stars in our Galaxy (though this number is certainly uncertain by a factor of at least two, because it is based on extrapolating what we know about stellar populations in our vicinity). Most of these stars are of lower mass and are much less luminous than the Sun.

The number of planets is even more uncertain. It now seems probable that most stars like the Sun have at least one planet, but we really don't know that much about the diversity of planetary systems, how typical something like the solar system is, or how planetary systems might change as a function of position in the Galaxy. We also don't know that much about planetary systems around the dominant (by number) very low-mass stars. They certainly can have planetary systems, but the fraction that do is still a work in progress.