Everyone has given plenty of good points here.

I will just respond to the original post with what I do in my household. My DD is well aware of what she can and can't touch that doesn't belong to her. But that's not the same everywhere she goes, so she wants to touch new things.

If she breaks something that does not belong to her, she straight away realises that it is broken and that is not what she meant to do. The only consequence for her that I enforce, is that she must take what she has broken (or I do if she is not able) to the person it belongs to and apologise. She is very downcast and quiet in her apology, but this to me means she understands to some extent and is sorry that it happened. When she has apologised, I then tell her we need to be very careful with other people's things and if she is not sure about touching something, come and ask Mummy. Realistically, she is too young to contain her enthusiasm for touching things, but I try to reinforce the message. Then I make sure I keep a very close eye on her when we are out and about. If I see her about to touch something that WILL break, I ask her to look with her eyes only and hold her hands behind her back. For some reason, that always works to hold her off until I'm close enough to move it!

At home, if she breaks something of mine, it's my fault. I shouldn't have left it where she could get it. She is still likely to say sorry to me, but I tell her it was an accident (as long as it was) and Mummy shouldn't have left it where it was. If deliberate, see above!

I should add though, I don't have a destructive child. She is not physical in her response to things, but very verbal. I try to line up my expectations with her capabilities.