I have found, through the years, that when someone asks me this question, it's usually being asked by someone who obviously CAN'T keep one.
This is obvious because the next thing out of their mouth is the secret that they themselves were told not to speak of.
I have found the best response for me is "sometimes" ...
I will usually get a puzzled look from this person, followed by their next question.
"What do you mean by that?"
Then I can explain.
It all depends on the type of secret.
One type may be gossip.If it's about someone OTHER than you, then it's probably gossip and I wouldn't want to hear it or believe it anyway.
The other type is, If it IS about you, Then I probably CAN keep it, unless the secret contains something about you harming yourself or someone else. Those secrets I can't keep for very long. And neither should anyone else.
With this being said ... Which type is your secret?