My boss and I were discussing the types of projects that newbies might want to tackle on their own time, if they aspire to working on some of the components that our team (Windows Security) owns.  He first gave an example that was much more exciting than that though - video games - since that was his job in a former life. 

He said, to paraphrase, "everyone wants to work on video games, right?  Well what would you ask someone to do to prove him/herself before taking on real work?"  He gave the following list.

1.  Write Breakout.  There's an input loop.  I also infer (I have no background in games) that there would be some challenge in getting the rendering to run smoothly as well, even if it's just running in a window.

2.  Then write Asteroids.  Remember linear algebra?  Now you get to use it.

3.  Then render your face on a cube.  Maybe put it in the middle of a "hallway" perspective like Wolfenstein.

After he listed those, I thought, wow how cool!  I don't even want to work on games, but those sound like cool projects.  I'd even do #1 or #2 just for kicks.  It's actually kind of an interesting way to think about an established technology area - what are the smaller projects that someone should do in order to ramp up?  For security/crypto/smart cards:

1.  Hash and digitally sign some data.

2.  Ditto, but with a certificate.

3.  Ditto, but you have to enroll for the certificate (programmatically, of course), and using a smart card.  The end result should be a signed PKCS#7.

Etc.