I very nearly responded to the OP several times... but then I realized my answers just kept sounding egotistical (I naturally compartmentalize, so secrets are no big deal to me... which disqualified me from answering... because I have a lot of secrets that don't bother me one iota). Since my secrets don't bother me, it DQs me.
But what do I consider to be a secret? 2 quotes first:
"The only way 3 people can keep a secret is if 2 of them are dead."
"A secret can be a little bit broached the same way a girl can be a little bit pregnant. It's either secure or it isn't."
So there's a Tier 1 secret: something NO ONE else knows.
Tier 2 is a secret I've learned but don't tell anyone ever, as they're not my secrets to tell.
Tier 3 is a need to know secret. One I've learned and only tell those that need to know. These are often occupational secrets.
Tier 3.5 is discretion. People who don't need to know may well know, but not many.
Tier 4 are dangerous secrets. I tell them at my own discretion.
Tier 5 are personal secrets. I also tell them at my own discretion. A family quote comes in handy here "You don't have to lie, but you don't have to run around shouting the truth, either."
Tier 6 are fun secrets. Surprises. And they're temporary.
Tier 7 aren't secrets... they just aren't common knowledge. Two examples amongst hundreds; 1) My finances. They are my own business. I'll often talk about them, but no one else (aside from the tax man) has a right to that info. Typically only the people closest to me are shared any info about my finances. 2) I've been raped. I have no problem talking about it. But I also don't tell everyone I meet that I've been raped. Most people in my life don't know, but many do. There is no "closeness" level associated with knowing. I really have no problem talking about it, and a stranger and I are as likely to have a conversation as a close friend.
What is great, however, is free will. I CAN share any of the above tiers at any time. I just don't. There is no way to bind another person's mouth (even blackmail, gag orders, & confidentiality agreements -all essentially the same thing - threats as to what will happen if a secret is told), so the only way for a secret to EVER be absolutely secure is if everyone who knows about it is dead, and all evidence annihilated. Which is practically impossible. Hence trust.
I'm personally pretty trusting, in a pessimistic sense, so I only ever trust others with secrets if I don't mind the entire world knowing.