1. The most common mineral of the Earth's continents—the world we spend our time in—is quartz, the mineral SiO2. Nearly all the sand in sandstone, in the deserts of the world and on its riverbeds and beaches is quartz. In granite and gneiss, which make up the majority of the deep continental crust, quartz is the most common mineral. BUT,
2. If you consider it as one mineral, feldspar is the most common mineral and quartz comes in second, especially when you consider the whole crust, continental plus oceanic crust. Feldspar is called a group of minerals only for the convenience of geologists. The seven major feldspars blend smoothly into each other, and their boundaries are arbitrary. Saying "feldspar" is like saying "chocolate-chip cookies" because the name embraces a range of recipes—in chemical terms, feldspar is XZ4O8 where X is a mixture of K, Ca and Na and Z is a mixture of Si and Al. To the average person, even the average rockhound, feldspar looks pretty much the same no matter where it falls in that range. And also consider that the rocks of the seafloor, the oceanic crust, have almost no quartz at all but abundant feldspar. So in the Earth's crust, feldspar in the most common mineral. BUT,
3. The Earth consists of a very thin rocky crust on top of a very thick rocky mantle. Compared to the mantle, the crust is small enough to ignore. And the most common mineral in the mantle is olivine. (The Earth's core doesn't count because it's liquid iron, which is not a mineral.)
If you get quizzed on this, look carefully at the wording of the question before you answer, and be prepared to argue. My official answer is number 2.