The diameter varies considerably depending on the type of equipment used. In the mid west US, shallow holes are usually done with one of the following:
3.5" O.D. solid flight auguers
3.25" I.D. hollow stem auguers
or
4.5" I.D. hollow stem augers.
The O.D. on these hollow stem augers about about 8" and 10" respectively.
There are also larger hollow stem auguers.
For deeper holes you have mud rotary drilling with bits starting at about 4" diameter and going up.