There's nothing wrong with crying.
But I don't think one should cry on front of somebody who needs someone with strength. If somebody's having a meltdown, say, it wouldn't help the person with the meltdown if YOU were crying as well. You have to keep a stiff upper lip in these instances.
Also: if somebody close to you is in great pain in the hospital, I don't think it would be taken too well if you were crying, despite you being in good health and not in the hospital.
Also: if somebody's depressed and you're not, it wouldn't make sense to cry over some trivial thing.
If I see someone crying in the street, I know it's none of my business--but I feel the urge to try to comfort the person, anyway.
What I hate, though, is "crocodile tears"--crying to manipulate, to get what one wants. I've had people try that on me all the time. Sometimes it succeeds, sometimes it doesn't.