They can make you turn on your pc and go through your files. We stopped flying with laptops in 2011.
A government office charged with defending civil liberties has declared that warrantless border searches of laptops do not raise civil liberties issues. The Office for Civil Rights and Civil Liberties at the Department of Homeland Security recently released an executive summary [PDF] of its findings, but it has refused to release the details of its analysis.
The Fourth Amendment protects Americans against unreasonable searches by domestic law enforcement, but the courts have long held that our Fourth Amendment protections are more limited when we travel internationally. Border agents can conduct random searches of passengers' luggage looking for contraband at the border. No warrant, or even reasonable suspicion of wrongdoing, is required.
The government has interpreted this rule as extending to data on electronic devices. If you travel with your laptop, the government can turn it on and rifle through your digital files. The American Civil Liberties Union has sued to stop this practice, arguing that the Fourth Amendment requires officers to have some reason to suspect a crime has been committed before snooping through travelers' personal data.
http://arstechnica.com/tech-policy/...rrantless-laptop-searches-at-border-are-a-ok/