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Stuart's code is very nicely written, and provides much to a learner, but it didn't work for me. Fixed versions are too long for just a comment, so here they are.

Python 2

The exact version I use: 2.7.3

import operator
OPTIONS = {
 'divide': operator.div,
 'multiply': operator.mul,
 'add': operator.add,
 'subtract': operator.sub
}
def user_input():
 while True:
 try:
 return input("Number: ")
 except ValueError:
 print("NOPE...")
def get_operation():
 while True:
 operation = raw_input("Multiply/Divide/Add/Subtract: ").lower()
 try:
 return OPTIONS[operation]
 except KeyError:
 print("Not an option.")
def play_again():
 while True:
 again = raw_input("Again? Yes/No: ").lower()
 if again == "yes":
 return True
 elif again == "no":
 return False
 else:
 print("Nope..")
while True:
 operation = get_operation()
 x = user_input()
 y = user_input()
 print operation(x, y)
 if not play_again():
 break

In Python 2, input returns an integer, so int(input(...)) is redundant, and inputting string (for operation and going again) fails. The later is fixed by using raw_input.

Python 3

The exact version I use: 3.2.3

import operator
OPTIONS = {
 'divide': operator.truediv,
 'multiply': operator.mul,
 'add': operator.add,
 'subtract': operator.sub
}
def user_input():
 while True:
 try:
 return int(input("Number: "))
 except ValueError:
 print("NOPE...")
def get_operation():
 while True:
 operation = input("Multiply/Divide/Add/Subtract: ").lower()
 try:
 return OPTIONS[operation]
 except KeyError:
 print("Not an option.")
def play_again():
 while True:
 again = input("Again? Yes/No: ").lower()
 if again == "yes":
 return True
 elif again == "no":
 return False
 else:
 print("Nope..")
while True:
 operation = get_operation()
 x = user_input()
 y = user_input()
 print(operation(x, y))
 if not play_again():
 break

The obvious error here was the last print statement: it's a function in Python 3, so print operation(x, y) had to be replaced with print(operation(x, y)).

The less obvious one is operator.div which doesn't exist in Python 3, but was instead replaced by operator.truediv and operator.floordiv. In the spirit of this program, I assumed that the former is what was intended.