If I may add a small point to Steve's excellent post (and something it took me a while to grasp):
The difference in time between the line-to-line and line-to-neutral voltage peaks is also why 120 + 120 = 208, and not 240, in 208/120-Y systems. Unlike the hots of a single-phase 240/120 system (180 deg. apart), the opposing peaks are not rising and falling simultaneously (120 deg. apart).
Using any one phase's voltage peak as a reference point, the voltage peak of the previous (or next) phase is already on the way back down (or still rising), so the phase-to-phase voltage is not twice the phase-to-neutral voltage.
Since there are only two points used to measure a voltage difference, it still looks like a symmetrical sine wave, rather than a lop-sided wave similar to a 2-cylinder engine with an uneven firing order. This is the part I used to have trouble with.
Logic seemed to dictate that, with two points peaking 120 and 240 degrees apart, the waveform would be very un-symmetrical. However, electricity doesn't work that way. We instead get a sine wave with an algebraically-derived voltage.
This is why an understanding of mathematics is so important to electrical theory. We may not need to know the math to do the physical work, but, as we see here, it can indeed matter when we have to do our own engineering.
[This message has been edited by Larry Fine (edited 10-25-2006).]
