My prediction is that SOPA and PIPA will pass in pretty much their current form (if they haven't already); the "write your Congressman" campaigns led by EFF, Wikipedia, and others, will have a negligible effect at best. However, I also predict that, in practice, SOPA will not be used to shut down any major website, such as Twitter or Youtube, though a non-trivial number of startups, personally hosted blogs, and other smaller websites will be taken down. Instead, the media industry will forge a deal with Google, Twitter, Facebook and other website providers, wherein the media industry receives an easy mechanism to take down whatever content they want at the click of a button -- in exchange for a promise to never use the SOPA nuclear option against the website provider (*).
I also predict, though with lower probability, that at least one major court challenge will be brought up against SOPA/PIPA shortly after its inception. Should such a challenge be brought, I expect to see a drawn-out legal battle that spans several years and ultimately goes nowhere (other than a settlement, perhaps).
Once SOPA passes, I expect alternative DNS providers to put up a token resistance, then fall in line, bowing down to "financial incentives", previous obligations, and outright legal intimidation. Alternative network infrastructure, such as Tor or Freenet or some new tool, will see a minor surge in popularity. If they really do take off (which I doubt), they will be quickly shut down in the name of fighting piracy, but an underground community of alternative network users will always exist.
I am very, very certain, however, that the average American internet user (and voter) will neither notice SOPA, nor care about it one way or the other.
(*) UMG claimed to have such a deal already in place, but it looks like they lied.
What about international effects? To my knowledge all the main DNS servers are located in the US, meaning that SOPA will apply to internet users in all countries...seems like other governments might take exception to that.
Referring, of course, to the proposed U.S. legislation which could cause severe damage to the Internet—at least, that's what a lot of people are saying. See, e.g., this Open Letter From Internet Engineers to the U.S. Congress (the first signatory listed is Vint Cerf). On Wikipedia, people including Jimbo Wales are discussing strategies as extreme as blanking the entire site (except for an explanatory message) to get people's attention, and thereby perhaps incite them to action, such as calling their Congressional representative.
I just happened to find out about all this a few hours ago, being someone who tries to avoid distractions like most kinds of news, so possibly others here with similar habits will appreciate having it called to ther attention. Or possibly they won't. But to those of you who possess relevant kinds of expertise:
(I think this subject can be discussed without political advocacy, in which I am mostly not at all interested anyway. It just looks like a practical problem to me.)
Edited to Add: I forgot to include a fourth bullet point:
It seems to have been assumed by many commenters, nevertheless.