There are several types of machine guns (machine pistols, submachine guns, assault rifles, Squad Automatic Weapons / light machine guns, general purpose machine guns, heavy machine guns, and so forth) and many different actual models made that fit into each of those groups.
Each manufacturer has set the cyclic rate of fire purposefully to achieve a certain firing characteristic. Many small machine pistols fire at extremely high rates of fire. (Over 1,000 rpm.) Some submachine guns fire at very low rates of fire. The US M3 "Grease Gun" fires at only around 400 rpm, which is about as fast as a very good pistol shooter can empty a 1911 handgun. Most assault rifles fire at a middling rate of 600-800 rpm. Belt-fed GPMGs are a mixed bag, with the German MG38s and 42s, known for blistering rates of fire of up to 1,700 rpm. The US M2 heavy machine gun is available in several versions from 450 rpm up to over 1,000.
With the slower operating guns (M3s, some Uzis, M2, etc.) you can indeed squeeze off one round at a time, with the gun on fully-automatic mode. By about 600+ rpms, you'll be limited to two shot bursts or more. The speedier guns (1,000+) are going to put 3, 4, 5+ downrange before you can get off the trigger, generally.
Machine pistols, most submachine guns, and assault rifles usually have a semi-auto setting allowing you to fire one shot for each trigger pull if you want. Most of the other styles of machine gun do not, but they generally aren't intended to be fired in a precision manner, either.