2 Answers
+ 6
For a beginner figuring out on your own (no cheating ;) how to write a simple recursive method, like a factorial - is already a solid achievement.
Or a program that defines a class and its methods, manipulates its attributes depending on user action (a comprehension of OOP).
Just how beginner we are talking about?
+ 3
if you're a beginner just in Python, not in programming, a nice challenge would be using libraries 'email' and 'smtplib' to write a simple command-line app to send an email. =D
It's not that hard and not that simple. And gives you a nice idea of what python can easily do for you. Also gives you an opportunity to use many of Python features.
p.s.: Both libraries, 'email' and 'smtplib', are standard. Access python 3 docs for more details.