What are some simple and informative beginners projects?
You've come to the right place to find out! It's a good idea to search for previous questions. One trick is to click a tag, like [beginner], then organize the returned results by clicking one of the headings: 


  about the beginner tag | faq | top users | hot answers | new answers | synonym


Clicking "hot answers" gives a bunch of results, of which these look promising:


What are the best hardware hacking magazines?
Learning Electrical Engineering
What are the ways I can make my circuit communicate with a computer?
What are the best beginner project using an arduino


In my opinion, digging into one of the Arduino kits is a great way to learn electronics. You have to work on fundamental electrical issues, like which way to plug in an LED and what value resistor to use with it, at the same time as successfully using a complete microcontroller implementation.

Here's another great project to get you started, with plenty of got'chas and complicated electrical schtuff, Adafruit's Mintyboost. It is a boost regulator, which is much more complicated and exciting than those linear regulators. Understanding how this project works will leave your classmates in the dust, and is essential knowledge later in your career (as a professional or hobbyist).