What SOPA and PIPA are attempting to do is force the private sector to screen out web sites or references or links to those web sites that offer torrent seeds or direct downloads of copyrighted material in countries where copyright laws are mostly ignored. In these countries, there's virtually no retail market because the average income of the population is so low, so there's a thriving black market that includes duplication of product packaging as well as the product itself. The copyright owners can't really do anything about this situation, and they don't care unless those pirated products make their way into countries where there is a retail market.
One initial issue with these proposals were provisions that would penalize USA companies like internet service providers for not actively screening out all DNS links to web sites in foreign countries declared to be pirate sites. The DNS clause was removed from SOPA, I don't know about PIPA.
Another issue is that any web site that allows its users to post text or data, such as a forum, chat room, web hosting service, or any web site with a search feature (bing, google, yahoo, ...), ... , could be penalized for not screening all posted content that could contain copyrighted material or links or torrent seeds, including multiple levels of indirection, ..., to copyrighted material or a description of how to do this or reveal some some trade secret.
Youtube tries to screen uploads, but just about any song can be found on youtube and downloaded. Youtube videos could contain text or speech in a video with information on how to access copyrighted content, such as a link or a search term. In some cases, such as clips from movies or music, eventually the video will get removed, or if multiple infractions occur, the account shut down, but then another one will spring up to replace it. However one common result of including music as part of the background of a video, is that youtube places an ad on the video and sends the proceeds to the copyright owner, or to godigital whichs owns a service that auto-screens youtube videos and files "matched third party content" claims to allow those ads to be placed giving a portion of the ad revenue to the copyright owner. Apparently this system is somewhat abused, making false claims to generate revenue from those ads.
My guess is that one of wikipedia's concerns would be the cost of trying to screen every bit of content added to wikipedia. Who would maintain an up to date list of every link, DNS, text description, ... that could be used to access pirated content?