New study suggests that children without regular bedtimes have more behavioral problems.

Researchers from University College London recently completed a long-term study of  babies born in the UK in 2000 to 2002, which regularly surveyed parents about sleep and behavioral problems. After analyzing data for over 10,000 children they discovered that children without a regular bedtime tended to score worse on a measure of behavior problems such as acting unhappy, getting into fights and being inconsiderate.
In three year olds, close to 20 percent of parents said their child sometimes or never went to bed at a consistent time. That fell to 9 percent among five year olds and 8 percent for seven year olds: at seven  those without a regular bedtime scored an 8.5, on average, based on their mothers' reports. That compared to scores between 6.3 and 6.9 for kids who had a consistent bedtime before 9 p.m.
The assessment is scored from 0 to 40, with higher scores indicating more problems. Researchers said one to two points represents a small or moderate difference, but is "meaningful."

Children with attention-deficit/hyperactivity disorder or an autism spectrum disorder were not included in the study. Teachers of seven year olds were also asked to report on their, and gave worse scores to children who didn't have a regular bedtime. Although the researchers accounted for other parent characteristics and family habits, it's still possible kids' behavior problems weren't directly caused by irregular bedtimes.

Nonetheless, the effects that a regular sleep schedule have on your "biological clock" have been well documented. Yvonne Kelly, who led the study says that "If you are constantly changing the amounts of sleep you get or the different times you go to bed, it's likely to mess up your body clock. That has all sorts of impacts on how your body is able to work the following day." 

Kids whose parents said they had non-regular bedtimes on every survey growing up had the most behavioral issues, but when children went from having a non-regular bedtime to a regular bedtime on the following survey their behavior scores improved.

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References:
Pediatrics (online October 14, 2013)
Non-regular bedtimes tied to kids' behavior problems (Reuters)