Sorry, this morning I've been in a bit of a hurry.
Here is an improved schematic and an explanation. I'll try to keep it simple:
The resistor R (100kOhm) "generates" a current from the battery's plus contact. If the alarm loop is closed, this current flows directly to the battery's minus contact. The transistors therefore are in the OFF state and the buzzer is silent.
If the alarm loop is broken, the current can no longer flow directly to the battery. Instead it flows into the base of the transistor Q1 (use one as CocaCola suggested). This current is amplified by the gain of Q1 (approx. 100, for this circuit the value is not too relevant). In this improved version there is a second transistor Q2 which amplifies the output current of Q1 a second time, thus giving an overall current amplification of 100*100=10000 (if you want to know more about this circuit google >darlington circuit<). Assuming 1 9 V battery and a base-emitter voltage drop for each transistor of 0.6 V, the current through the resistor is approx. (9 V - 2*0.6 V)/100 kOhm = 78µA. This current is amplified by a factor of approx. 10000 which gives an output current of Q2 of 10000*78µA = 780mA *). A typical buzzer should require a lot less current, so this circuit supplies enough power.
End of simple explanation.
Here a few more notes, in case you're interested:
This is only a very general principle. This circuit, for example is notz tamper proof at all. A wood-be thief could just short circuit the alarm loop by a string of wire that bypasses the object to be protected and then cut the original wire. Thus circuit wouldn't notice. A more elaborate circuit could use special wire with a defined resistance for the alarm loop an measure the resistance. If the resistance is either higher than expected (cut wire) or lower than expected (bypassed wire) an alarm would sound.
To save energy, the alarm loop could be operated in a pulsed manner, e.g. only be tested every 100 ms or so, thus requiring less current during the idle time.
Also a practical alarm circuit could have a timer which would allow the owner of the alarm to disarm the alarm before it starts to wail (in case he forgot to disarm the alarm before opening the loop. A blinking LED could be an indicator allowing the owner to disarm the alarm within the first 5 to 10 seconds of opening the loop).
Also you'd want to have a battery supervision so you can be sure the alarm will operate at least as long as your bike is partked (just an example). Because an empty battery makes the whole effort null.
And last not least you need a tamper proof case for the circuit.
Plus, plus, plus...
Harald
*) footnote: This doesn't mean that 780 mA will flow through the buzzer. Only that this is the upper limit. The circuit will not supply more current (at least not while maintaining the voltage across the buzzer), but will happily supply less current if the buzzer is satisfied with less.