The majority of our food is actually digested during sleep, so the common argument that "eating late at night is bad because our metabolism [slows or shuts down] during sleep" is incorrect. With that said, there is a correlation between night eating, low self-esteem, reduced daytime hunger, and weight gain among people who are already obese or prone to obesity, however, this correlation does not necessarily imply causation (i.e., the act of eating a late meal does not necessarily provoke these conditions). It may simply be the case that the types of foods that people prefer to eat late at night are less healthy. There is still much debate on the subject, however, many scientists agree that meal frequency, as opposed to time, is one of the best predictors for weight gain. For example, the time between meals is highly correlated to one's waist size. This makes some intuitive sense, since eating more, smaller meals will help regulate insulin levels, and spikes in insulin levels (which can be caused by large meals and/or large gaps in time between meals) have been linked to weight gain.
I remember hearing on NPR a year or two ago about a study which specifically tried to test the claim that eating late at night is unhealthy. The study concluded that there was absolutely no correlation between the proximity of mealtime to sleep and weight gain, other than the fact that people tend to choose to eat more unhealthy foods late at night. I can't seem to find a reference to that study, however.
Update: A newer study followed the eating and sleeping patterns of 52 subjects over one week. They found a correlation between "late sleepers" (i.e., people who go to sleep late and wake up late) and high body mass index, and that eating after 8pm was associated with higher body mass index. A New York Times article summarizing the results of the study makes the further claim that eating late at night leads to weight gain, however, I disagree with that claim on the grounds that correlation does not imply causation. In fact, that study noted:
Late sleepers consumed more calories at dinner and after 8:00 PM, had higher fast food, full-calorie soda and lower fruit and vegetable consumption.
Therefore, I think the results of the study can be interpreted to mean that there is a correlation between eating/sleeping late and a poor diet.
Furthermore back in 2006, the same research team conducted a study on monkeys in which they were fed a diet similar to the average (i.e., high-fat) diet common in the USA. The only variable was the time of day that the monkeys were fed. With all else remaining constant, the researchers found no correlation between weight gain and time of feeding.
It was really interesting to see that the monkeys who ate most of their food at night were no more likely to gain weight than monkeys who rarely ate at night. This suggests that calories cause weight gain no matter when you eat them.