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I just read this on another message board:
If you know which breaker each outlet is on, it's easy. Breakers that are directly adjacent to each other (above/below or left/right) are on different legs. Breakers that are diagonal are on the same leg.
Is this true?
It's written really poorly, so it's neither true nor false.
In most modern panels, breakers that are directly next to each other horizontally are on the same leg. Breakers directly above or below are on a different leg.
Another answer explains the split phase normally used in residential electrical service. This picture
from answer to 46960 explains how breakers basically do alternate as you say, which leg of the service they draw from.
Note that there are breakers that attach two circuits in a single space, etc., so it's a little more complicated, but if you keep in mind what the bus looks like underneath, you'll understand what's going on.
A single split-phase center tap transformer supplies most homes in the USA as 120/240V. Condominium homes are generally 3-phase WYE 120/208.
With a center tap split-phase, the secondary sinusoidal wave is physically split in to two 180° halves by the neutral.
Thus, on a single split-phase panel there are two busses that are designed to distribute the loads/breakers as equally as possible....but much of the load balancing is fined tuned by the electrician during the installation, as lights generally have much higher loads than outlets.
Have a look at this answer for more information and illustrations. *Note: the link is mainly about split buss panels but may be relevant for your question.
The illustration below shows the basic wiring of the common single phase transformer and how it supplies individual appliances in a home. Note how the single phase is split in to two 180° potentials with the neutral at the zero potential.
