What is the minimum time to consider with a connecting flight in the USA?

Most US airports (IAD, DTW, JFK, ATL, etc.) have separate terminals for international and domestic flights - arrivals and departures. And more often than not, the two terminals are separated by at least a (internal) transit ride. Moreover, in addition to the immigration lines, all international transit passengers are required to collect their baggage AND clear customs. The former is highly unpredictable... So, considering -

 1. Alighting the aircraft
 2. Immigration
 3. Baggage Collection
 4. Customs
 5. Re-deposition of baggage for the onwards flight, and
 6. Making your way to the "domestic" terminal,

I would budget at least 3 hours between your connections.

Just to be clear are you talking about a single ticket or buying two separate tickets? If you have a single ticket with an international segment followed by a domestic segment, the airline will accommodate you on the next flight if the international procedures (immigration, customs, etc.) take too long and you miss your connecting domestic flight. Of course the next flight could be much later or full, but you will get there eventually. If you are buying separate tickets there is no guarantee at all that you can board the next flight if you miss your connection. In general, I wouldn't try to schedule a very tight international connection, but if your connecting domestic destination has frequent flights, it may not be too risky.

At least at JFK when you land you can get some vouchers (don't remember how they are actually called) that allow you to skip the immigration line if you have a connecting flight. Don't know if it's the case in other (smaller) airports. In this case all the immigration formalities (provided there are no issues) shouldn't take more than 20-30 minutes.

I haven't tried this myself, but when we were landing (flying in from Europe) flight attendants informed us that we can get these vouchers and go through a separate short queue for passengers going to connecting flights. I saw a sign for this at the immigration check and there was no line there whatsoever as opposed to a huge line for general public. This definitely applies to non-US citizens and I think to US citizens too. It's just a separate line that in the end goes to the same immigration officers. You are just allowed to cut the standard line through a separate entry because you have a ticket to your next flight.

Edit: Just checked and this was in Terminal 4 of JFK in April, 2011.

Beware that sometimes the airlines have some stupid minimum connection times. More than once I've been offered a totally impossible connection on an international to domestic situation. The limiting factor for me has actually been baggage, not immigration.

You always have to claim your checked baggage at the first point of arrival and carry it through customs. You can then generally drop it (it will already be properly tagged) on a belt somewhere near the door you come out of customs.

Note that this means you have to wait for your bag (it's about 50/50 whether I get to the carousel before my bags--note that you have already cleared immigration at that point) pass through customs (usually very quick but occasionally they're picky as I'm normally coming from a country of concern to the ag people) and get it on that belt outside before the cutoff for checking bags for your connecting flight.

There have been multiple times I could have made the close flight (I walked by the gate where it was going to board) but I couldn't have gotten my bag on it.

Note, also, that you always exit customs into the non-sterile area. This means you have to clear security before you get your next flight. These days that can be a substantial delay.

I will never consider anything less than 2 hours on international -> domestic. I've had the computers book connections as close as 70 minutes.

I travel quite often from Europe (Visa Waiver citizen) to the US with a connecting domestic flight, usually through ORD, EWR or CLT.

From my experience the biggest unknown factor is the immigration. I experienced wait times between 15 minutes and 2.5 hours. The wait time at the immigration is highly dependent on no. of open counters, no. of aircrafts arrived (i.e. passengers arrived) and general organisation at the airport.

As it's pretty difficult to to forsee these factors, I always book flights with a connecting time of at least 3 hours and I book ALWAYS the international and the domestic flight with the same airline.

So far I have never missed a connecting flight and if this would happen the airline has to rebook me. Sometimes I had some annoying wait times, because immigration, baggage collection, customs and check-in (and security checks) to domestic flight was surprisingly fast, but usually with the 3h-rule it's OK.