It's actually 120V/~208V. If you're feeling frisky, you can confirm this by going around between random pairs of outlets in your house and comparing the right slots from two different outlets until you find a pair of them that are out of phase from each other.
Fundamentally, the power grid is based on three phase power. Typically, the average telephone pole will have four power wires on it, and one or two thick bundles of phone line or maybe cable TV, I dunno. Three of those four power lines are the three phase electricity, and the fourth is the common neutral line that is ideally near 0V, but typically fluctuates a bit.
Only three out of those four lines enter your house. One is is the neutral line, the other two are just two of the three power lines. Those two power lines are not 180 degrees out of phase, they are 120 degrees out of phase. If they were 180 degrees out of phase, the math is simple: it's obviously just 240V. Since it's 120 degrees out of phase, you end up with a sine wave that looks something like 120\(sin(x)-sin(x+pi\2/3)). (only you need to adjust it for frequency) If you're better at your trig identities than I am, you can calculate that out exactly, but for simpletons like me I just plug it into my calculator and find a local maximum of 207.846 something.
(note: In the US, we use neutral and ground to refer to the common center of the three phase power, and the wire that is buried in the ground near your house, respectively. In the UK, I think they call these two wires ground and earth, respectively. Note that the term "ground" has a very different meaning (read: one of them can kill you, the other one keeps you safe) depending on the context.)
This is not correct for the majority of US households.
Two of the phases DO NOT run to the house, a typical US household service is split-phase. The primary winding in the transformer at the pole connects between a single phase and ground, and the secondary winding is center-tapped to provide a 'neutral', with 120v on either side of the neutral. The voltages are indeed 180 degrees out of phase.
Your test would show 220-240v in the vast majority of US-based residential situations.
The 120/208 you are referring to is when all 3 phases are fed in to a WYE transformer that has 3 120v secodary windings fed from a center point, which becomes the neutral. With a WYE transformer, each phase gets 120v to ground/neutral, and the phase-to-phase voltage indeed peaks at 208v due to the 120 degree rotation between phases. This is typically only found in large residential(600+ amps), and medium to large commercial and industrial buildings with 3-phase service.
Another method would be using a 'Delta' transformer, in which one of the phase-to-phase windings are center-tapped, similar but a little different than the single-phase residential service. The two phases on either side of that center-tap will be 120v to neutral, but the 3rd phase will be 208v to netural/ground. This is usually called the 'wild' leg and is often used to power lighting loads.
That's interesting, and I don't doubt that you have seen a system like that, but it sounds more like what could be expected in an industrial setting with 3-phase power.
The few houses that I was involved in wiring of in the states were definitely "split phase" systems, which work like the GP describes. In those, three current-carrying wires come from the transformer - two ends and a centre tap from one winding. Those are wired in the breaker box so that the house has two circuits that are 180* off from each other, giving 110V on either circuit, or 220V between the two "hot" legs. There's a better description at https://en.wikipedia.org/wiki/Split-phase_electric_power.
