Madeira has very little crime and the worst that is likely to happen to you is a case of sunburn or a hangover. Violence against tourists is very, very unusual.
Pickpockets and bag snatchers are not usually a problem. However, as with anywhere in the modern world, be aware of people that brush up close to you or jostle you, and don't leave bags and camera equipment unattended.
Common sense at all times should spare you any grief.
If you are the victim of theft, you must report it to the police and get a report, if you want to make an insurance claim. If your passport is stolen or lost, you must contact the local consulate to get a replacement issued.
There are not many nuisances in Madeira. Maybe the odd car parked on the pavement or the odd mosquito in the height of summer but nothing that should interfere with the enjoyment of your holiday.