In his speech to the Commonwealth Club of San Francisco, the FBI director said he had received an e-mail supposedly from his bank that looked "perfectly legitimate." The e-mail asked him to verify some bank information, but he quickly realized that might not be such a good idea. "Just a few clicks away from falling into a classic internet phishing scam," Mueller said.

"[I] definitely should have known better," the FBI chief said. He changed passwords and tried to convince his wife it was nothing more than a "teachable moment," but she wasn't buying it and banned him from online banking.

Mueller's self-deprecating anecdote was part of what the FBI calls "a major address" in the ongoing "'cyber arms race.' Law enforcement forces and criminals are competing to stay one step ahead of each other in what the agency describes as an "ever-expanding virtual frontier."

On Wednesday, the FBI announced that Operation Phish Phry has resulted in the arrest of some 50 individuals in California, Nevada and North Carolina, and nearly 50 Egyptian citizens. The defendants are facing charges that include computer fraud, conspiracy to commit bank fraud, money laundering, and aggravated identify theft. The agency said the suspects victimized "hundreds and possibly thousands of account holders" by stealing their financial information and using it to transfer about $1.5 million to bogus bank accounts.

In a statement, the FBI said that during the two-year investigation, which was led by its Los Angeles office, "we worked closely with the Secret Service, the Electronics Crimes Task Force in Los Angeles, state and local law enforcement and our Egyptian counterparts -- the first joint cyber investigation between Egypt and the United States."

As Mueller was addressing the audience in San Francisco, the FBI was rounding up the suspects. "It's the largest international phishing case ever conducted," he said.

Mueller went on to warn people about revealing too much of their lives online. Youthful indiscretions posted on your photo page "come back to haunt you" during a job search, he said. "I do not have a Facebook profile," he said.

He also issued a warning to hackers engaged in phishing and other types of cyberfraud. "You hack, you get caught. You are going to jail," Mueller said. "You are not going to get a good job afterward. You are going to be identified as a person who has broken the law."

Despite the FBI's efforts, "we are still outnumbered by cybercriminals," Mueller said, which is why the public must be vigilant about "protecting your home computer with firewalls, anti-virus software and strong passwords."

Said Mueller: "We all have a responsibility to protect the infrastructure that protects the world."

(Read CNET News.com's tips for avoiding phishing scams.)

Watch Mueller's speech here: