Just how safe is Bitcoin?

Using Bitcoin, a person can buy almost anything, from computers to houses to coffee. Bitcoin wallets are used to send transactions to and from a user. Wallets have both a public key, which anyone can see (quite similar to an email address), and a private key (similar to a password). Without this private key, Bitcoin cannot be accessed.
But how secure is Bitcoin? The Bitcoin protocol itself is secure due to blockchain technology. However, the same cannot be said for the threats posed to accompanying sites and services.