What popular apps or websites have a privacy policy that should concern me and might affect the degree to which I use those sites or apps?

It depends on your privacy standards. For example, if you don't want  your data to be sold to third parties,like advertisers who want to use your web browser history for retargeting purposes, you should stop using half the internet or use some scripts to avoid to be tracked. Another issue that concerns many people is the waiver to the right to sue. Big sites are adopting clauses that make you waive the right to join a class action, and force you to follow an arbitration procedure. Skype recently did that: https://www.docracy.com/doc/diff?originalId=0am1glu0a0q&revisedId=0xgv5wfb72v#tab_summary If a site collects user generated content (e.g. Quora), the terms will usually include something that allows them to use your content for free, forever. Some people might be ok with that, but if you are a professional photographer, you might not want to use sites like Instagram. Mobile apps have additional privacy issues, including geotagging information that they can sell, and people's telephone numbers (Whatsapp is a notorious bad player: http://www.reuters.com/article/2013/01/28/us-whatsapp-privacy-idUSBRE90R0T520130128)

All search engines. You ask questions to search engines that you'd never ask your spouse or minister, so it's ultra-important that search engines not keep your search history, or share it with others, even with different divisions of the same company. There are a bunch of smaller search engines which make better privacy an important feature. These include: blekko, ixquick, and duckduckgo. Of these three, the only one with its own crawl+index is blekko.