Web archiving services play an increasingly important role in today's information ecosystem, by ensuring the continuing availability of information, or by deliberately caching content that might get deleted or removed. Among these, the Wayback Machine has been proactively archiving, since 2001, versions of a large number of Web pages, while newer services like archive.is allow users to create on-demand snapshots of specific Web pages, which serve as time capsules that can be shared across the Web. In this paper, we present a large-scale analysis of Web archiving services and their use on social media, shedding light on the actors involved in this ecosystem, the content that gets archived, and how it is shared. We crawl and study: 1) 21M URLs from archive.is, spanning almost two years, and 2) 356K archive.is plus 391K Wayback Machine URLs that were shared on four social networks: Reddit, Twitter, Gab, and 4chan's Politically Incorrect board (/pol/) over 14 months. We observe that news and social media posts are the most common types of content archived, likely due to their perceived ephemeral and/or controversial nature. Moreover, URLs of archiving services are extensively shared on "fringe" communities within Reddit and 4chan to preserve possibly contentious content. Lastly, we find evidence of moderators nudging or even forcing users to use archives, instead of direct links, for news sources with opposing ideologies, potentially depriving them of ad revenue.