So I'm wondering how to determine the number of standard outlets a single circuit should be able to have. I imagine this will also depend on the kind of wire being run as well as the amp rating of the breaker. So, using standard gauges, and a typical breaker, like 20 amps, how many outlets could a single circuit supply?

Within the residential world, there is no restriction on the number of receptacles on a circuit.

In the commertical world, however, each yoke is estimated at 180 VA per outlet.

Really depends on what you plan to put on the circuit. For a 20 amp breaker on a 12 AWG wire the non continuous load is 2400 watts. A small space heater and an iron will hit almost 2400 so determine need first. Treadmills run about 15 to 17 amps themselves.