According to a January decision by the California Supreme Court, police can search your mobile phone without a warrant after taking you into custody. Like many blows to the Fourth Amendment, the case involved the victimless crime of drug dealing. In People v. Diaz, the court ruled that police did not violate the rights of Gregory Diaz, a suspected Ecstasy dealer, when they read his text messages.
U.S. Supreme Court precedents such as U.S. v. Robinson (1973) and U.S. v. Edwards (1974) imply that police may search anything on an arrestee's person, both to protect officer safety and to find evidence of a crime. But another precedent, U.S. v. Chadwick (1977), seemed to support Diaz's position that the search of his cell phone required a warrant.
In that case, the Court declared that a search of luggage in the trunk of a suspect's car more than an hour after his arrest was too far removed from his person and the time of the arrest to be legally valid. By contrast, the majority in Diaz decided that the cell phone was "immediately associated with [the defendant's] person" and therefore searchable.
Dissenting Justice Kathryn Werdeger argued that a mobile phone, particularly a smart phone, which is essentially a portable computer, is qualitatively different from a jacket pocket or pack of cigarettes. In 2009 the Ohio Supreme Court likewise decided that the sheer amount of information available from modern phones distinguishes them from a small container on one's person.
Various federal district courts have agreed with the California Supreme Court that a cell phone search "incident to arrest" is constitutional. It seems likely that the question eventually will be resolved by the U.S. Supreme Court.