Never had a serious incident in Aruba, probably because I'm anal about keeping things in safe and not carrying a purse when out and about. Everything goes in the safe and if I need money I make sure I have pockets and stuff everything in them. Son't worry about what I look like with bulging pockets...my stuff is safe and that's what matters.
We have however had stuff stolen out of our glove compartment...out by Charlie's in SanNic. It was our own fault, parked in back and I think one of the vagrants watched us put things in it. NOthing valuable...couple pairs of sunglasses and a brush or 2. It happened in the parking lot across from the Paddock one afternoon also...another pair of sunglasses....took 2x before I learned my lesson. But with all that being said I still feel safe there and have never feared walking around with or without my husband.
You just have to remember to not make yourself or belongings a target....