Here is a more robust way to input the number. It check if it can be added. Moreover I added the positive and negative number.
# -*-coding:Utf-8 -*
print ("Keep inputting numbers different than 0 and each one will be added together consecutively.")
print ("Enter a and the total will be displayed on the screen. Have fun.")
sum = 0
x = ""
while type(x) == str:
try:
x = int(input("Value : "))
if x == 0:
break
sum += x
x = ""
except:
x = ""
print ("Please enter a number !")
print ("Result : ", sum)