The Bitcoin protocol is very safe. In fact 100% safe. Why? Because in Bitcoin protocol, there exists blockchain which acts like a public ledger and it contains the bitcoin address of every bitcoin holder and hence any transaction can be easily verified.
So far, after 8 years, there have been no instances of the protocol not working. 3rd parties have been hacked (notably Mt. Gox), feds have stolen website's bitcoin (silk road), but the protocol itself is solid. The security of your money, for the first time in recent history, is left up to you, the user. You own your bitcoin in addresses which you have the private keys to. Do not trust someone else with those keys, such as mt. gox, silk road, coinbase, an exchange, or whatever. That defeats the purpose of bitcoin. Encrypt your wallet with a strong password, backup your wallet, store the majority of your coins offline, don't let your computer get viruses. If you do that, then your coins are safe and no one can take them away from you. Silk road coins were stolen by the feds because they were able to gain the administrators decryption passwords. Don't trust a third party, learn how to secure coins yourself.
It's been pored over by countless computer security experts and there are no known protocol exploits. The whole world can be expected to agree on who owns what. This is the beauty of Bitcoin.
When you hear concerns about Bitcoin security it is usually about the security of a particular private key for a Bitcoin address, which is analogous in many ways to a password. If you are very careful about your personal computer security it is possible to offer strong guarantees about your security in Bitcoin!