Create panel > Geometry button > Standard Primitives > Object Type rollout > Sphere button
Create menu > Standard Primitives > Sphere
Sphere produces a full sphere, or a hemisphere or other portion of a sphere. You can also "slice" a sphere about its vertical axis.

The defaults produce a smooth sphere of 32 segments with the pivot point at its center.
Radius—Specifies the radius of the sphere.
Segments—Sets the number of polygonal divisions for the sphere.
Smooth—Blends the faces of the sphere, creating a smooth appearance in rendered views.
Hemisphere—Increasing values progressively will "cut off" the sphere, starting at the base, to create a partial sphere. Values range from 0.0 to 1.0. The default is 0.0, producing a full sphere. A setting of 0.5 produces a hemisphere, and 1.0 reduces the sphere to nothing. Default=0.0.
Chop and Squash toggle creation options for Hemisphere.
Chop—Reduces the number of vertices and faces in the sphere by "chopping" them out as the hemisphere is cut off. Default=on.
Squash—Maintains the number of vertices and faces in the original sphere, "squashing" the geometry into a smaller and smaller volume toward the top of the sphere.
Slice On—Uses the From and To angles to create a partial sphere. The effect is similar to lathing a semicircular shape fewer than 360 degrees.
Slice From—Sets the start angle.
For both settings, positive values move the end of the slice counterclockwise; negative values move it clockwise. Either setting can be made first. When the ends meet, the whole sphere reappears.
Smoothing groups are assigned to sliced spheres as follows: The surface of the sphere is always assigned group 1; the bottom, when Smooth is on, gets group 2. Facing the pie-slice surfaces, the cut on the left gets group 3, and the cut on the right gets group 4.
Material IDs are assigned to sliced spheres as follows: The bottom is 1 (when Hemisphere is greater than 0.0), the surface is 2, and the slice surfaces are 3 and 4.
Base To Pivot—Moves a sphere upward along its local Z axis so the pivot point is at its base. When off, the pivot point is on the construction plane at the center of the sphere. Default=off.
Turning on Base To Pivot lets you place spheres so they rest on the construction plane, like pool balls on a table.
Generate Mapping Coords—Generates coordinates for applying mapped materials to the sphere. Default=on.
Real-World Map Size—Controls the scaling method used for texture mapped materials that are applied to the object. The scaling values are controlled by the Use Real-World Scale settings found in the applied material's Coordinates rollout. Default=off.