I have heard a lot of buzz about distant planets that could potentially be second homes for human existence, but what is that approximate number?
There is currently only one planet known to be capable of supporting human life, and you're on it.
Several planets have been found in the region in which we expect water to be liquid on much of the planet. Of these, only one fits the criteria of being Earth-sized and well placed in the habitable zone: Kepler 186-f
However we know nothing about it's atmosphere (or lack of one). The star is a red dwarf, so it could be subject to dramatic solar flares. The planet is rather colder than earth, so could be in a perpetual "snowball world" state, depending on the composition of the atmosphere and the strength of the greenhouse effect. The atmosphere would be very unlikely to be even close to breathable, and it is nearly 500 light-years from Earth, so could not be reached in a reasonable amount of time, even with much more advanced propulsion.
At the moment we can't usually detect most Earth-like planets in the habitable zone of brighter stars like the sun, though the probably do exist and may be common.
You may be interested in the number of habitable zone planets. These are planetary-mass objects in a sort of "Goldilocks" region from their respective stars: This region is just right, given adequate atmospheric conditions, to possibly permit the existence of liquid water on the surface. That's not a surefire sign that the planet is capable of supporting humans, but it's certainly a good start.
Scientists Kane and Gellino have tabulated such information at the HZ Gallery. As of Sep 2015, the site assesses nearly 1600 exoplanets of which 62 spend their time entirely within the habitable zone.