On the American wheel, there are many examples where this rule is violated. On a European wheel, this is only violated where the 5 sits next to the 10 (both low numbers). The wheels are also structured so that the low numbers (1-18) and the high numbers (19-36) should alternate as much as possible. On both wheels, the red and black numbers alternate around the wheel, although if you removed the zeroes, the American wheel would have consecutive reds and blacks. The numbers are arranged in a different order on each wheel but there are some similarities in the patterns. On an American wheel you can expect to lose 5.26% (if you are interested in the mathematics of roulette, the video at the end will show you how these odds are calculated). On a European wheel you would expect to lose, in the long run, 2.7% of any money you bet with.
This is important as it doubles the advantage for the casino.
Notice that the American wheel has two zeroes.