This is the guy who famously and cryptically warns Caesar to "beware the Ides of March" (1.2.21). The "Ides of March" refers to March 15, the day Julius Caesar is assassinated by the Roman conspirators. Even though he gets to speak the coolest line in the play, nobody pays any attention to the soothsayer (except the audience, who knows all about how the historical Julius Caesar was stabbed in the back that day).
The soothsayer's warning raises an interesting question about fate and free will. If Caesar had actually heeded the warning to "beware the Ides of March," could he have changed the course of events that day? On the one hand, the soothsayer's warning about his impending doom (along with all the other creepy omens in the play) suggests that Caesar's fate is already decided. On the other hand, why would the soothsayer bother warning Caesar if there was nothing he could do to prevent his death? For more on this, see "Themes: Fate and Free Will."