Version 1.0 If the door knob is touched (from the other side of the door) the alarm goes off.

I wired a 10 uf capacitor in series with a 1 mega-ohm resistor from 5v to Analog0 like this:

The Arduino is hanging on the doorknob by the loop in the wire. AnalogRead records the change in values. If the wire is touched directly then analogRead drops quite a bit, if the doorknob is touched on the other side of the door, it drops just a little bit.
I also wired a potentiometer so that the sensitivity can be adjusted and the alarm will be activated by that small drop in value.
//When someone touches the doorknob the analogRead value from the wire drops a bit.
int sensorPin = 0;
int ledPin = 13;
int sensorValue = 0;
int pot;
int sensor;
void setup() {
pinMode(ledPin, OUTPUT);
Serial.begin(9600);
}
void loop() {
sensorValue = analogRead(sensorPin); //the doorknob sensor wire
delay(10);
pot=analogRead(5); // the potentiometer is connected to analog 5
Serial.print(sensorValue); //sensor wire value
Serial.print(" ");
Serial.println(pot); //potentiometer value
delay(100);
if(sensorValue<pot){ // this allows you to turn the potentiometer to a sensitive borderline value
// when someone touches the knob it dips just below the pot value
digitalWrite(13,HIGH); //the led (alarm) lights up. This could be replaced by a buzzer
delay(100);
digitalWrite(13,LOW);
}
}
For the next version:
I don't have a wide variety of capacitors and resistors to experiment with so there may be a better combination.
Also, the LED could be replaced by a buzzer.