What is the purpose of "finally" in try/catch/finally

The syntax will change from language to language, but this is a general question.

What is the difference between this....

try
{
     Console.WriteLine("Executing the try statement.");
     throw new NullReferenceException();
}
catch (NullReferenceException e)
{
     Console.WriteLine("{0} Caught exception #1.", e);
}       
finally
{
     Console.WriteLine("Executing finally block.");
}

and this....

try
{
    Console.WriteLine("Executing the try statement.");
    throw new NullReferenceException();
}
catch (NullReferenceException e)
{
    Console.WriteLine("{0} Caught exception #1.", e);
}        
Console.WriteLine("Executing finally block.");

I keep seeing it being used, so I assume there's a good reason to use finally, but I can't figure out how it's any different from just putting code after the statement since it will still run.

Is there ever a scenario where finally doesn't run?