The State of Ohio passed a law against anonymous pamphleteering, tried to fine someone, and was taken to court. A forerunner of all of these writers was the pre-Revolutionary War English pamphleteer 'Junius,' whose true identity remains a mystery. As the court pointed out, anonymous political speech has been around for quite a while. It was very popular with this nation's Founding Fathers and was used extensively during the campaign to ratify the Constitution. Knowing this, then, makes the majority opinion of the Supreme Court rather easy to understand.
Anonymity is a shield from the tyranny of the majority.
The right to remain anonymous may be abused when it shields fraudulent conduct. But political speech by its nature will sometimes have unpalatable consequences, and, in general, our society accords greater weight to the value of free speech than to the dangers of its misuse. So, if the FEC tries to regulate political speech on the Internet, we'll be within our rights to tell them to go away and mind their own business.