Can an image flashed in the middle of a video for a single frame (as in this hoax by Vicary), induce a specific behavior in people? An example would be the supposed use of this to get people in theaters to buy snacks. Is there any research demonstrating this to be effective or ineffective?
Reading this article might be a good one.
In short, it tells of the start of all this "single frame" theory, namely that research that made you drink cola / eat popcorn. This was not good research, if there was any research at all.
There is however a lot of media coverage and 'urban myth' stuff going on.
That last part triggers me to check Snopes for the subliminals for the pocorn story :)
To go beyond the popcorn-myth, still in the same article (emphasis mine, do also check the background of the title, the 'cargo-cult' story is too great to miss):
During the past few years, I have been collecting published articles on subliminal processes-research that goes back over a hundred years (Suslowa 1863) and includes more than a hundred articles from the mass media and more than two hundred academic papers on the topic (Pratkanis and Greenwald 1988). In none of these papers is there clear evidence in support of the proposition that subliminal messages influence behavior. Many of the studies fail to find an effect, and those that do either cannot be reproduced or are fatally flawed on one or more methodological grounds, including: the failure to control for subject expectancy and experimenter bias effects, selective reporting of positive over negative findings, lack of appropriate control treatments,...
The article states a lot of references in the bottom, and the conclusion is clearly that there have been attempts to proof, but no evidence found, that subliminal messaging works.
In short: Sometimes they do something.
Showing someone who has a strong phobia of spider for a split second can produce a rise in blood pressure without the person being consciously aware of having seen a spider.
There was even a study that used subliminal images of spiders to combat the phobia of spiders.
You don't need to be consciously aware of a stimulus to be effected by the stimulus. In most cases a stimulus that raises conscious attention is however much stronger than a stimulus that doesn't.