All the good points have been covered so its only really down to the chat now.
Yes an alarm will deter the casual thief. But if it just makes a noise and has no connection to a security firm, a quick smack with a hammer will be enough for those that "earn a living" from other peoples property.
Our shed is connected to the alarm on the house. The last time the postman leaned up against the door, I got a call from the rent a cop and was home to investigate. They to had been by to have a look. Nothing was nicked so it must of just been a false alarm. Point is it worked...(?)
The truth is that what ever you do to make your shed or house more secure if the buggers want to get in they will. The best way to keep them out is not having things laying about that can be seen from the windows.
As Colin pointed out, and a policeman will tell you, the game is make your house more secure than the one next door and you will be OK.
If you are building a wooded shed, before you put the outside covering on (Recommend plywood sheet, screwed on) re-bar netting, yes the stuff they use in cast concrete, will prevent even a chainsaw cutting a hole in the wall.
If you put bars in the window, use tube instead. just put a hard steel bar lose inside. If they try cutting the "bars" in the window once they get through the pipe, and hit the solid bar, it will just spin round and act as a roller preventing them from sawing through!
I like colins idea, build it bigger and use it as a kennel for the pet wolves...
Ian M