May the police search me without a warrant?

That depends on whether you are under arrest. If the police have lawfully arrested you, they are permitted to search you. They also are allowed to search the area under your immediate control (also known as your wingspan, or where you can reach). This may include, for example, the glove box of your car.
If you are not under arrest, the police generally are not permitted to search you. There are a number of important exceptions to this rule. The police may search you if you consent, but doing so limits the range of your defense in later proceedings. Your consent, for example, will make it difficult to challenge the legality of the search at a pretrial suppression hearing. Many people feel they should consent in order to show the police they have nothing to hide--but what you consider insignificant, such as a piece of paper with a telephone number, may be incriminating if it links you to a crime.
The police also can search you for weapons if a police officer reasonably feels in danger.
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