How many Watts can I safely draw from a typical US home circuit for Bitcoin mining? Suppose I have a mining rig that draws 1,200 Watts.  How many of those mining rigs can I run on a standard US home circuit?

Do I need a special outlet?

What is the risk of an electrical fire?

What other safety precautions should I take?
There isn't a single "standard" for residential circuits in the U.S. but there might be a typical circuit, such as 20 amps.

As far as plug connections, don't use light-duty extension cords; make sure they are rated for high amperage, say 20amps.  Generally if you are plugging directly into an outlet then the total power drawn can be done safely up to 80% (rule of thumb) of the level the wiring is rated for.

If the circuit breaker is 20 amps and the circuit is using the proper gauge wiring for that and was wired properly, then you should be able to draw 16 amps safely from it.

16 amps * 120V = 1,920 watts.

So you could add a smaller capacity rig on the same circuit but you cannot have more than one of those 1.2 kWh rigs on what might be a "typical" residential circuit.

[Disclaimer: I'm not an electrical engineer nor an electrician but I play one on Bitcoin stackexchange.]