I would say that it depends on the length of the spear. A unit using sarisa would be far more formidable than a unit using Hasta. Halberds would be in the middle but are used quiet differently from spears. Pikes again would be formidable to face as a single fighter against a unit. If said fighter was surrounded, the situation is even worst.
So, let's say your "spear" is 5 meters long. You have a circle of circumference of
2 * pi * 5 = 31.4. Assuming that a human (with amour) takes a "face" of .3 meters (sideways posture), you have
31.4/.3 = 104 people around your lone surrounded (and soon to be very dead) fighter.
Or, as Sean Cheshire says: If we use a single handed spear, then the calculation is
2 * pi * 2 / .3 = 41 people - still enough to do a lot of damage.
Technically, you could have any number of spheres (or an ovoid for more precision) of spears. From that point of view, the tip of the spear is the limiting factor. Those all need is an approximation of the dimensions of the target (minus 3/5 cm to allow for lethal penetration of each tip). This would depend on the shape of the tip, and how tightly you could pack them -- round tips are worst in this regard than square ones. This would massively increase the amount of fighters utterly surrounding the lone wolf.
Note 1: I would give a small penalty to the surrounding fighters as they are going to hinder each other a little (depending on training) but the final result is still going to be same: dead lone wolf.
Note 2: Combat in more than 3-dimensions is left as an exercise to the reader.