Depends on the animal.
Do you remember these guys:

Siegfried and Roy. Two of the biggest acts ever to appear in Vegas. They did magic with live animals like tigers, lions and others. That is until once night in 2003 Roy, I think he’s the one on the left, was mauled by one of the tigers.
Supposedly the tiger got spooked and attacked him leaving him terribly injured. He claimed later that the tiger tried to save him as it pulled him off stage.
They would raise these cats from the time they were young. Living with them and even sleeping with them in the same bed until the cats were year old. But even then they were wild animals and an animal like that can turn on you in an instant.
You can never truly tame a wild animal even if you raise it from birth. Their instincts are still very very real and dangerous.
EDIT: Comments turned off as everybody keeps saying the same things. Yes I said that wild animals can’t truly be tamed. No need to keep repeating that.
This one?

Yes, absolutely.
This?

No, I would say absolutely not.
But let’s be clear about something. Wild animals don’t have masters. You’re not the boss of them, even if you keep them in captivity.
(Edit: folks taking this too literally, and those who ‘knew a guy with a tame tiger and he didn’t get eaten’ will be deleted at this point. This is more about statistical likelihood and safety than certainty. It doesn’t mean every person with a Nile crocodile will be eaten. It just means that no matter how you raise it, an adult Nile crocodile will probably at least try to eat you at some point).
Depends on the individual and the species. But if you’re talking a very large animal, your big problem isn’t whether it will prey on you, but whether it will kill you by accident in a moment of irritation or clumsiness, due to not realising how comparatively weak you are. Even large horses have been known to kill people by accident by e.g. swaying against them in a narrow passage.