Should I have my security alarm system monitored ?

By all means, yes.

A monitored system won't stop someone from breaking in, nor will it usually allow for the police to "catch them in the act" but it does decrease the likelihood of someone staying around your property for extended periods with an elaborate noisemaker going off.

In the case of most systems, a monitored system would also provide (depending on programming and service provider) a manual panic button, a manual fire alarm, as well as duress signaling. It would also lower the chance of repeat break ins if somebody watching the premises to see if someone responds to the alarm going off. It will also notify somebody should you be away on vacation and allow them to take appropriate steps to secure your property should the need arise. It also allows the police to meet someone (if not yourself) on the property who is designated to be a key holder to allow them to enter and walk the premises, as most police jurisdictions will only require further investigation on obvious outward signs of break in.

Your homeowners insurance rates will usually decrease for having a monitored alarm, possibly even further by having a monitored fire alarm or critical condition monitoring, such as CO, flood, or freeze protection. Usually the discounted rates will cover the cost of monitoring, even allow for a considerable savings depending on the risk of your property.

Many localities will not respond to a self-monitored alarm, nor will they accept an automated direct dial from your house or alarm should an event happen. Also, should you consider self monitoring and the alarm goes off, are you going to rely on a friend or neighbor to respond to your property should the alarm go off.

Also of interest, lots of communities, especially gated ones, have their own private monitoring facilities, as well as roving patrols.

If you are having a system monitored, preferably professionally, but even if you are self monitoring, make sure all points are covered and local ordinances, including alarm registration, audible alarm cutoff times, even dialer shutdown or inhibit are met as failure to comply with ordinances usually will result in steep fines after a few false alarm dispatches.