Why is it bad?
The Stop Online Piracy Act is H.R.3261, and the Protect-IP Act is S.968.
The intent of both pieces of legislation is to combat online piracy, giving the Attorney General and the Department of Justice power to block domain name services and demand that links be stripped from sites not involved in piracy. The problem is that the legislation, as written, is vague and overly-broad. For one thing, it classifies internet sites as "foreign" or "domestic" based entirely on their domain name. A site hosted abroad like Wikileaks.org could be classified as "domestic" because the .org TLD is registered through a U.S. authority. By defining it as "domestic," Wikileaks would then fall under the jurisdiction of U.S. laws. Other provisions are worded even more poorly: in Section 103, SOPA lays out the definition for a "foreign infringing site" as one where "the owner or operator of such Internet site is committing or facilitating the commission of criminal violations punishable under [provisions relating to counterfeiting and copyright infringement]." The problematic word is facilitating, as it opens the door to condemning sites that simply link to other sites.
The most obvious implication of this is that search engines would suddenly be responsible for monitoring and policing everything they index. Google indexed its trillionth concurrent URL in 2008. Can you imagine how many people it would take to double check all of them for infringing content? But the job wouldn't end at simply looking at them — Google would have to continually monitor them. Google would also have to somehow keep track of the billions of new sites that spring up daily, many of which would be trying to avoid close scrutiny. Of course, it's an impossible task, so there would need to be automated solutions. Automation being imperfect, it would leave us with false positives. Or perhaps sites would need to be "approved" to be listed. Either way, we'd then be dealing with censorship on a massive scale, and the infringing sites themselves would continue to pop up.
But the problems don't end there; in fact, SOPA defines "Internet search engine" as a service that "searches, crawls, categorizes, or indexes information or Web sites available elsewhere on the Internet" and links to them. That's pretty much what we do here at Slashdot. It's also something the fine folks at Wikipedia and reddit do on a regular basis. The strength of all three sites is that they're heavily dependent on user-generated content. Every day at Slashdot, readers deposit hundreds and hundreds of links into our submissions bin. Thousands of comments are made daily. We have a system to surface the good content, but the chaff still exists. If we suddenly had a mandate to retroactively filter out all the links to potentially copyright-infringing sites in our database, we wouldn't have many options. We're talking about reviewing hundreds of thousands of submissions, and every comment on 117,000+ stories. And we're far from the biggest site around — imagine social networks needing to police their content, and all the privacy issues that would raise.
Small sites and new sites would be hurt, too. A website isn't a single, discrete entity that exists on its own. A new company starting up a site would have to worry about its webhost, registrar, content provider, ISP, etc. The legislation would also raise significant financial obstacles. New companies need investments, and that would be much less likely (PDF) if the company could be held liable for content uploaded by users. On top of that, if the site was unable to live up to the vague standards set by the government and the entertainment industry, they could be on the receiving end of a lawsuit, which would be expensive to fight even if they won (and such laws would never, ever be abused). It's hard to conceptualize the internet without noting its unrivaled growth, and SOPA/PIPA would surely stifle it.