Sentinel Loop Python

The de facto way of handling this is to use a list rather than throwing away the individual scores each time.

scores = [0] # a dummy entry to make the numbers line up
print("Enter the scores: ")
while True: # We'll use an if to kick us out of the loop, so loop forever
    score = int(raw_input("Score {}: ".format(len(scores)))
    if score < scores[-1]:
        print("Exiting loop...")
        break
        # kicks you out of the loop if score is smaller
        # than scores[-1] (the last entry in scores)
    scores.append(score)
scores.pop(0) # removes the first (dummy) entry
average_score = sum(scores) / len(scores)
# sum() adds together an iterable like a list, so sum(scores) is all your scores
# together. len() gives the length of an iterable, so average is easy to test!
print("The average score is {}".format(average_score))

You want to keep asking the user a new input while its a greater number each time. You can use a list to keep every score entered and then use the sum built-in function to do the work for you:

scores = []
while True:
   current_size = len(scores)
   score = int(raw_input("Score %s" % (current_size + 1)))
   # Check if there's any score already entered and then if the new one is 
   # smaller than the previous one. If it's the case, we break the loop
   if current_size > 0 and score < scores[-1]:
       break
   scores.append(score)

# avg = total of each scores entered divided by the size of the list
avg = sum(scores) / len(scores)
print "The average score is %s" % avg

Your code has various issues and won't even run. Here's a working version that does approximately what you seem to want.

Managing old and new values using a while loop is a common idiom in coding and worth practicing.

EDIT: I buggered up the order of the lines of code myself. The code now gives the correct averages.

scoreTotal = 0
loopCounter = 0
scoreCount = 0
newScore = 0
oldScore = 0
print("Enter the scores:")
newScore = int(raw_input("Score 1: "))
while newScore >= oldScore:
    scoreTotal += newScore
    scoreCount += 1
    loopCounter += 1
    oldScore = newScore
    newScore = int(raw_input("Score " + str(loopCounter + 2) + ": "))
averageScore = float(scoreTotal) / float(scoreCount)
print scoreTotal, scoreCount
print "The average score is " + str(averageScore)

Following Raymond Hettinger's talk and Amir's blog post http://blog.amir.rachum.com/blog/2013/11/10/python-tips-iterate-with-a-sentinel-value/

In [1]: def loop():
   ...:     old = 0
   ...:     while True:
   ...:         new = raw_input("gimme")
   ...:         yield new > old
   ...:         old = new
   ...:         

In [2]: l = loop()

In [4]: list(iter(l.next, False))
gimme1
gimme2
gimme0
Out[4]: [True, True]