In the TV movie Time Element, a man goes to sleep in New York in 1958 and wakes up in a Honolulu hotel room in early December, 1941. At the hotel bar, he meets a sailor from the USS Arizona and tries to convince him not to return to his ship later that night. Of course everyone in the bar thinks he's crazy, and he's soon taken in to custody to be given a psychological examination.
When asked by his examiners who the president is, he at first answers, Eisenhower, then remembering it's 1941, corrects himself, saying Roosevelt. But when asked who the vice president is, he answers incorrectly Harry Truman, bringing stares of wonderment from the interrogators. He tells them that FDR will die and Truman will succeed him, then turns around and asks them if they know the meaning of terms such as rock and roll and Sputnik. He manages to escape immediately afterwards. Most of the interrogators conclude that he's a nut, but one of them is convinced that he is not crazy.
To pick a more recent example, say you contacted Logan airport on 9/10/2001 and told them under NO circumstances allow Mohammad Atta (and the other pilots) on board those planes.
Perhaps call in a bomb threat to close down the airport.
Sure you "might" prevent 9/11, but then you'd also know about other upcoming tragedies, plane crashes, bombings, politics etc.
SOMEONE would find you and they'd be VERY interested in just how you know that stuff.
They'd probably torture you for information.
Or even kill you.