What type of wire should be used for wiring alarm contacts? Can phone wire be used?
Probably so, but more information is needed before the question can be answered. Have you bought a commercially made system? If so, the manufacturer should have a recommended size/type of wire. If you're buliding your own, be aware that there are more than one sizes of wire that's sold as telephone wire. Some are braided, some are solid. None of them is made to handle 110v AC.
Genral rule of thumb is stranded wire, it dosent break as easy. You should use a 22gau 2 cond (usually a 4 cond is used because price is not much more and its better to have the extra just in case) for your doors and windows, a 22-4 for motion detectors, Glass Breaks, and other powered devices. Smoke detectors come as 2 or 4 wire devices, a siren wire should be 18 gau 2 cond as well as the transformer wire. The key pad depending on the system can be any where from a 2 cond to a 8 cond. Some other devices can have there own special requirements check the installation specs. If you plan on being monitored a 22-6 is a good idea to the phone company box(2 conductors for phone in 2 for phone out and 2 for a tamper.