Why would Wikipedia show set external links as rel="nofollow"?
One of the ways search engines determine what Google calls “PageRank” is by the number of incoming links, with more weight given to sites with high page-ranks (NB: I will use this term as the generic word to mean how a search engine prioritises how the results are displayed).
This has resulted in so-called “link spam” where multiple sites have been created for the purpose of linking from them to try and boost the page-rank of the linked site.
Since Wikipedia is one of the most highly ranked sites on the internet, and it allows anyone to create links from there, it would be a ideal place for people to create pages and links for the sole purpose of boosting their site’s page-rank.
By enforcing “nofollow” tags, it tells the search engines that these links are worthless when it comes to considering their value to the linked site. This means the incentive to fill Wikipedia with link-spam is basically eliminated.
There's a couple of reasons why any website (including Wikipedia) that welcomes user content today would make links as no-follow.
Links can become outdated and may even return error pages (example: error 404) to the user when accessed. A web page that contains at least one link to an error page is not a good page to be indexed on the Internet.
As someone mentioned, websites that allow users to publish content can potentially manipulate the ranking of the site and/or other sites by advertising links to any website (depending on what filters the website the guest is using has in place). As a concrete example, If a user publishes hundreds of links to vulgar and/or sex when the site has no relation to that, it may at the very least confuse search engine robots into believing the website has more to hide and that it can't be trusted on to deliver quality results that users expect to see.
In order for webmasters to protect themselves from fooling search engine robots, they will (or at least should) do one of the following when having user content published for the public to see:
They will put the content on hold while an actual person checks the content to see if its acceptable for the site then publishes it manually. This is the best option, however we are in the world where people don't have time to check thousands of paragraphs of content.
They will let the content be published right away but make every single link as no-follow, at least until the links are manually validated.
They will use automated filters to see if the content matches against certain words or phrases and if it does (or does not), then content will be rejected.
In any event, if the link doesn't add any value to any user or is not related to the website in any way, it should be made as no-follow, or better yet, the link should not be available at all.