The Bitcoin technology itself – in other words, the protocol and the cryptography – has a strong security track record, and the Bitcoin network is probably the biggest distributed computing project in the world.
Bitcoin’s most common vulnerability is in user error.  Just as in real life, you secure and protect your “wallet” – a bitcoin wallet is no different, and if you don’t, your money can be stolen.
You should be wary of services to store your money online, and you should be aware that most losses of bitcoin were the result of security breaches through such services.  Also, your bitcoin wallet should be just like your wallet you carry around with you – it should contain small amounts of cash or bitcoin.  You wouldn’t carry your life savings around in your wallet, and you shouldn’t keep all your bitcoin in your online wallet either.  If you wish to keep all your bitcoin online, at least setup several different accounts – they’re free, and you can reduce the risk of “keeping all your eggs in one basket.”
Offline wallets, or cold storage, will deliver the highest level of security for your bitcoin savings. It involves storing your wallet in a secure location that is not connected to the bitcoin network or the Internet. If handled and setup properly, an offline wallet can offer very good protection against computer vulnerabilities. Using an offline wallet along with backups and encryption, while leaving a small amount of bitcoin for buying or selling in your online account, or in several online accounts, is a good practice.