The simplest way to create a smooth sphere in Blender is to create a UV sphere. The problem with using a UV sphere is that you need a high number of rings and segments, say 128, to minimize stretching artifacts around the poles where the faces converge into one vertex. When the default settings are applied when creating an UV sphere, and a subdivision modifier is added, the artifacts become more apparent:
NB: To make the artifacts more apparent you can use a MatCap shader. Here, you can see which shader I selected in the dropdown menu:
Another problem with using a UV sphere is the topology which becomes an issue when you want to map an image texture using a UV map, made from the object's vertices. Fortunately, there is a better method of creating a perfectly smooth sphere with good topology, and it begins with a cube.
To make a perfect sphere, you will need to add a cube with Shift+A > Mesh > Cube. Add a subsurf modifier and increase the level of viewport subdivisions to 4.
You now have a perfectly smooth sphere with no visible artifacts ready for texturing. This kind of sphere is ideal for mapping an earth texture to.