For this one I used a potentiometer connected to analog pin 1 to control the brightness of an LED connected to digital pin 9.

Here's my code:

 

int val = 0;
int ledPin = 9;
int potPin = 1;

void setup() {
  //twiddle your thumbs
}

void loop() {
  val = analogRead(potPin);
  val = map(val, 0, 1023, 0, 225);
  analogWrite(ledPin, val);
  delay(30);
}

 

Here's a Fritzing pic of my circuit: