+1  A: 

Hello World!? :)

treznik
+3  A: 

You could always solve some problems on Project Euler. My favorite starter project, however, is usually a sudoku solver or tic-tac-toe bot.

Cybis
A: 

Print the first 100 prime numbers! And this doesn't mean...

Console.Write('3');
Console.Write('5');
Console.Write('7');

And so on...

Chalkey
A: 

Start the project you intend to use those skills for. There is always a certain amount of project setup, core library code that needs building. If you know programming you need to rebuild some similar knowledge. There is no substitue for the real thing.

Mark Redman
+1  A: 

I learned C with a simple implementation of Life, and its a decent project to exercise yourself in a new language.

Arkenian
A: 

Solve some programming puzzles.

  1. Programming Praxis.
  2. Project Euler.
  3. TopCoder.
  4. Facebook puzzles.

More on Google: programming puzzles.

BalusC
A: 

Recently, I've been looking at the code golf, homework, and beginner tags on SO for inspiration and simple/intermediate ideas.

JohnK813
A: 

I'm a fan of cletus' text-based adventure idea for starter projects.

Kaleb Brasee
A: 

My favorite is tic-tac-toe. It's simple enough so you can code it in a day, even in a new programming language, but complex enough so you can really use language features. You can use polymorphism (human/computer of players), higher order functions (for the minimax algorithm), IO (console based or graphical), you can play with various data representations etc.

nikie