Cuba is generally safer than most countries, with violent attacks extremely rare. Petty theft (eg rifled luggage in hotel rooms or unattended shoes disappearing from the beach) is common, but preventative measures work wonders. Pickpocketing is preventable: wear your bag in front of you on crowded buses and at busy markets, and only take the money you will need when you head out at night.
Begging is more widespread and is exacerbated by tourists who hand out money, soap, pens, chewing gum and other things to people on the street. If you truly want to do something to help, pharmacies and hospitals will accept medicine donations, schools happily take pens, paper, crayons etc, and libraries will gratefully accept books. Alternatively pass stuff onto your casa particular owner or leave it at a local church. Hustlers are called jinteros/jinteras (male/female touts), and can be a real nuisance.