The Journal of Advertising has published a study about how kids perceive online advertising. Short answer: they don't. Kids were found not to make much of a distinction between advertising and the content (games, videos, information) on the sites they visit. It's just all part of the same experience.
The last sentence in this excerpt will make you sad:
Ms. Stern and a colleague looked at the reactions of 112 fourth-graders who played "Be a Popstar," a game focused on the Honeycomb cereal brand that was available on Postopia, a site sponsored by Post Foods. The research found that the advertising notifications -- which the study refers to as "ad breaks" -- didn't succeed in communicating the commercial nature of the site to most of the children.
Some children played a version of the game with ad labels, and some played a version with the labels removed. When the children were asked to identify the source of the game, there were no significant differences in the responses of the two groups. Thirty-four percent of all participants said the site had been created by a pop star or celebrity -- the most common response. Some children even named particular stars, hypothesizing that the site was the product of, say, the Jonas Brothers. Only 10 percent correctly identified the source as the cereal maker or the Honeycomb brand.
In fact, researchers found that the children were more likely to believe that the site was trying to turn them into a pop star than that it was trying to make them want to eat Honeycomb cereal.