During my first month of learning python, I wrote a game to guess a number between 1 and 20 with six attempts. This simple game is good practice for a beginner. A better written and more advanced version can be found at http://housewifehacker.com/intermediate-guess-number-python-game.html. This example is written in Python 2.6.
import random
guessesTaken = 0
print 'Hello! What is your name?'
myName = raw_input() #get user name
number = random.randint(1,20) #random number between 1 and 20
print '%s I am thinking of a number between 1 and 20.' % myName
while guessesTaken < 6:
    print 'Take a guess.'
    guess = int(raw_input())
    guessesTaken += 1
    if guess < number:
        print 'Your guess is too low.'
    elif guess > number:
        print 'Your guess is too high.'
    else:
        break #breaks out of loop
if guess == number:
    if guessesTaken == 1:
        print 'Good Job, %s! You guessed my number in 1 guess!'
    else:
        print 'Good Job, %s! You guessed my number in %d guesses!' % (myName,guessesTaken)
if guess != number:
    print 'No. The number I was thinking of was %d' % number
