What is somebody who can "predict" or "see" into the future called?

single-word-requests

Solution 1:

In such a case you are prescient.

prescience

noun pre·science \ˈpre-sh(ē-)ən(t)s, ˈprē-, -s(ē-)ən(t)s\

the ability to know what will or might happen in the future

Solution 2:

A person who has:

Foreknowledge of an event, especially as a form of extrasensory perception. (ODO)

is precognitive (adjective):

The woman who stepped into my office was tall, leggy, beautiful - and bewildered, "How did you know I was about to knock" "Like it says on the door, I'm a precognitive detective.

Jack Hammett, Precognitive Detective

or has precognitive abilities/ability of precognition:

"He's been dead for ten years", she said.

"Er", said Windle, but the question was already there in his larynx, "I trust Mr. Cake is in good health?"

"It's okay. Oi speaks to him occasional," said Mrs. Cake.

"I'm sorry to hear that," said Windle.

"All right, if it makes you feel any better."

"Um, Mrs. Cake? I'm finding it a little confusing. Could you...switch off...your precognition...?"

from: The Reaper Man, by Terry Pratchet

(context: Mrs. Cake has the ability of precognition, so she answers Windle's questions before he has the chance to ask them.)

Solution 3:

Although the word "prophet" may have a religious meaning in some contexts, it can also be used to refer to a person with non-spiritual abilities to predict the future.

prophet