Alec Macgillivray (Twitter General Counsel, former Google attorney, Berkman Fellow) has a great post explaining how SOPA might impact everyday Americans:

The harm that does to ordinary, non-infringing users is best described via a hypothetical user: Abe. Abe has never even so much as breathed on a company's copyright but he does many of the things typical of Internet users today. He stores the photos of his children, now three and six years old, online at PickUpShelf* so that he doesn't have to worry about maintaining backups. He is a teacher and keeps copies of his classes accessible for his students via another service called SunStream that makes streaming audio and video easy. He engages frequently in conversation in several online communities and has developed a hard-won reputation and following on a discussion host called SpeakFree. And, of course, he has a blog called "Abe's Truths" that is hosted on a site called NewLeaflet. He has never infringed on any copyright and each of the entities charged with enforcing SOPA know that he hasn't.

And yet, none of that matters. Under SOPA, every single one of the services that Abe uses can be obliterated from his view without him having any remedy. Abe may wake up one morning and not be able to access any of his photos of his children. Neither he, nor his students, would be able to access any of his lectures. His trove of smart online discussions would likewise evaporate and he wouldn't even be able to complain about it on his blog. And, in every case, he has absolutely no power to try to regain access. That may sound far-fetched but under SOPA, all that needs to happen for this scenario to come true is for the Attorney General to decide that some part of PickUpShelf, SunStream, SpeakFree and NewLeaflet would be copyright infringement in the US. If a court agrees, and with no guarantee of an adversarial proceeding that seems very likely, the entire site is "disappeared" from the US internet. When that happens Abe has NO remedy. None. No way of getting the photos of his kids other than leaving the United States for a country that doesn't have overly broad censorship laws.