You can own Bitcoin, you can’t own your dollars.
People are always wondering how safe is buying Bitcoin if there are constant heists on exchanges and no website has perfect reputation. They draw analogy with the banks: which organisation can I trust to handle my money?
The right answer is: with Bitcoin you don’t need to hold your money on an exchange for longer than a minute. You wire your government currency to an exchange (bitstamp, coinbase, bitcoin-central, btc-e, kraken, btcchina), buy some bitcoins at a current price and move them hell out of there to your personal wallet. The exchange can be hacked next day, but it won’t matter to you. You are not storing money there anymore. Your private keys are only stored in your encrypted backups and only you know the password. As long as the applications you use are not infested by viruses or backdoors, and you have enough of separate physical backups, you are pretty safe. PS. Don’t use Windows!
Another question people ask: why can’t I simply use my Visa card like I do with the rest of my purchases? Or PayPal. The answer is because this money is never owned by you and all transfers are reversible. Bitcoin transaction is confirmed by the network and buried in the blockchain in 10 minutes. Visa transaction is reversible within 90 days. There were people who tried to sell Bitcoin (ultra-liquid asset that you can own) for PayPal (highly controlled asset that is owned by a chain of banks and payment processors). People grab your bitcoins and call PayPal to reverse a transaction (“someone stole my password!”).
People who start learning about Bitcoin should understand one thing. You don’t own your usual money. You may own paper bills to some degree, although, government does devalue them all the time by printing more of them and restricting movement of large enough sums. Your bank account you don’t own at all. Even wire transfers may get reversed, although, rarely. All your transfers are basically promises from one banker to another. The entire banking system is a complex network of mutual promises not backed by anything except desire to not break the law (yet another system of promises to reward or to punish). And these promises are being broken or revisited all the time on every level. Laws and regulations are not consistent even with each other, not only with every particular decision.
Bitcoin, on the other hand, is like air-thin gold on steroids: you can fully control your transfers and the entire network forces everyone to follow very strict rules to ensure validity of all bitcoins and the rate of their creation. The shitty C++ code of BitcoinQT (original and the most used client) is infinitely more compact, rigid, logical and consistent than all regulatory environment with millions of account managers in the entire financial system.
You can also own gold, but that ownership comes with huge costs and risks. Someone needs to guard the vault, transport the vault, verify the purity of the bars and coins. All of this makes it impossible to use gold in the global economy. Which is precisely why we arrived at the modern all-controlling banking system — it grew up out of the necessity to reduce costs of handling gold by entrusting it to the biggest vaults. To use gold as money you have to trust someone to store or transfer it for you. So you are back to the current very fragile system.
The only money you can truly own today regardless of the amount is Bitcoin.