My coins are associated with a brand new, never-sent-from address. To "forge" bitcoins would mean to get an unauthorized (by me) transaction from that address. First, the hacker would need to break hash function so badly as to be able to quickly reverse my address into the public key. Then, the hacker would need to break the digital signature algo so badly as to be able to reverse public into private key. All this is essentially impossible to happen without years of warning signs of weakened security of the two algorithms.

One thing to worry about is forging (replacing) public addresses with fake ones. Just think about all the donations and trades happening where person sending coins cannot easily be sure the website or email was not tampered with, and that he is sending coins to the correct address. This is not Bitcoin problem, this is the Web/email security problem. There are solutions, but for some reason general public generally doesn't care.