Several points have been raised in this discussion to which I would like to respond.
First, the normal 3-wire 120/240V North American service is most definitely single phase, NOT two phase. There are two "hot" legs on the supply, 180 degrees out of phase with respect to neutral/ground, but it is still a single secondary winding on the transformer. The180-degree difference comes about only due to the center-tap position of the neutral connection. Note that the primary of the transformer is still also just a single winding with only two connections, and whether that primary is connected between phase-and-neutral or between two phases of the HV line, it still has only a single sinewave applied to it. You need some sort of third reference point to even be able to measure any sort of phase difference.
Seombody mentioned a delta supply which has one phase grounded and whether that would be considered two phase. Such a system is commonly known as a "corner-grounded" delta, and it is still three phase. There are some 3-phase delta supplies which are ungrounded. Once again, the application of a ground connection to one phase to turn that into a corner-grounded delta doesn't alter the 3-phase nature of the supply -- it merely provides a reference point to ground.
One arrangement which seems to be uniquely North American is the FOUR-wire delta arrangement, also known by various names such as high-leg delta, wild-leg delta, red-leg delta, and so on. To visualize this system, start with a basic ungrounded 240-volt delta secondary, drawn with phase B at the top and phases A and C at either end of the horizontal winding at the bottom. Now, instead of connecting a ground to one phase as you would for a corner-grounded delta, put a center-tap on the A-C winding. Ground that center-tap, and extend it to the building as a neutral, giving the four wires.
You can now connect a 3-phase 240V delta load A-B-C as you would with the basic delta system, and you can connect a single-phase 240V load A-B, A-C, or B-C, as before. Thanks to that center-tap, you can now also connect 120V loads phase A to neutral -OR- phase C to neutral. The result of that ground placement, however, is that phase B will be at 208 volts with respect to neutral/ground, hence the various "high-leg" et al descriptions.
I understand that the 4-wire delta was once common for light commercial services, as it allows for 3-phase 240V delta equipment while also providing 120V for lighting and general small loads without having to resort to adding extra transformers or installing a separate120/240V service.
Turning to the east side of the Pond, we have several differences in the way distribution is handled. Speaking for the U.K., we tend to use one very large transformer to feed a whole section of a neighborhood rather than the much greater number of smaller transformers that would provide power to an American neighborhood with a similar number of houses.
Anywhere where there are more than just a few houses, you'll find a3-phase transformer with its secondaries feeding a 415Y/240V 3-phase 4-wire wye distribution network. Individual houses then get a 2-wire 240-volt single-phase service tapped from one phase and neutral, the load being distributed between the phases as evenly as possible. In towns, that same wye network can also provide 3-phase 4-wire service for commercial power.
It's possible for a VERY heavy domestic load to be provided with two or three phases, but extremely rare, and only likely to be found in a VERY large house which is all-electric. The standard 240V 2-wire residential service these days is 100 amps, which provides 24kW and is ample for most purposes. There are plenty of older services rated 80,60, and even 40A still in service. I've even seen an old 30A service as recently as two or three years ago, although they're pretty rare now.
We do also have single-phase transformers, most commonly found on poles in rural areas to serve one or two isolated houses or farms. These have a straight 240V secondary with one end grounded to provide a single-phase 240V service.
Finally, out here in the boondocks you can also find 3-wire single-phase 240/480V distribution where there are a dozen or two houses scattered along a road. The system is similar to the American120/240V arrangement with a center-tap neutral, except that each house still gets just a 2-wire connection to provide 240V and a single transformer will feed the whole lot. Although you won't find this system in towns, it's a convenient "halfway house" for some rural areas.
On the primary side of these transformers, everything here is connected between phases. In fact NONE of our HV lines have a neutral run with them, so three-phase primaries are always delta-connected, and the primary on a single-phase transformer is connected across two phases of the HV. That primary supply to the final transformers is almost always 11kV (measured phase to phase), although there are still a very few local distribution networks operating at 6.6kV in a couple of areas. Thus a single-phase HV spur line has to be run as two "hot" phases.
As noted before, in Continental Europe 3-phase supplies into homes are very common, however, and to British and American minds they seem to take 3-phase to extremes. In France, for example, it's not at all uncommon to find a small house which has a full 3-phase 4-wire380Y/220V service, with the main breaker set to just 15 amps per phase! Arranging heating and cooking loads on a service like that can be quite a juggling act.
I've referred to U.K. supplies as 240V, but in fact we only finally standardized on 415Y/240V in the early 1970s. Prior to that, the nominal declared voltage varied from region to region, anything between 200 and 250V with corresponding 3-phase voltages (380Y/220,400Y/230, 433Y/250V, etc.).
As noted, we're OFFICIALLY now 400Y/230V to align with European standards, although in practice most areas haven't actually changed anything yet. They just juggled the old +/-6% tolerance to an assymetric +10/-6% so that we could declare ourselves to be 230V without changing anything!
We had several different frequencies in use across Britain in the early days. The push to standardize on the 50Hz that we use today came about with the plans for our "National Grid" in the 1930s.
Some parts of the American west coast also had 50Hz power in earlier times. I understand that the Los Angeles area was on 50Hz originally, and converted over to 60Hz in the early 1930s, complete with publicity programs to help get clocks and other synchronous devices changed. I've seen other references which suggest that some parts of California (and maybe Oregon and Washington too) had patches of 50Hz power until the 1950s, presumably in those places which generated locally and were not connected to any sort of statewide grid.
Other places have also used "oddball" frequencies. I was looking at some service manuals for old Garrard turntables (early 1950s) a couple of months ago, and noticed that they offered not only 50 and 60Hz motor pulleys but also 40Hz versions at that time. I found out from a contact "down under" that some parts of western Australia were using40Hz power at that time.
In Britain, DC supplies survived well into the 1950s and early 1960s in some urban areas (those older parts of cities which had been the first to get power). These DC systems used an Edison-type 3-wire distribution system, running at anything between 200/400 and 250/500V (this was before there was nationwide standardization of voltage). Normal domestic services were just 2-wire 200 to 250V, some houses tapped from the positive "outer," others from the negative. Commercial service could then get the full 3-wire supply so that they had 400-500V available as well.
One other odd DC system which we still have is that on the London Underground (subway) system. LU uses a 4-rail arrangement, at a nominal 630V DC. However the ground reference is set on a one-third/two-thirds arrangement, so that the positive conductor rail (located outside the running rails in the usual "3rd rail" position) is at +420 volts and the negative rail (placed centrally between the running rails) is at -210 volts with respect to ground.