Such questions should be Closed with the custom Off-topic reason: Questions on applications or application features that are no longer available are off-topic for Web Applications as no one will ever be able to make use of the answers again.
In some cases, such as Hotmail, there is a clear successor app. The tag for the retired app should be made a synonym of the successor. (Questions that are still clearly about the original app and not applicable to the new app due to different features, etc., should still be closed.) In extremely rare cases (e.g., Delicious) a web app may be resurrected and questions become viable again.
Below is a list of Web applications that have questions here, as well as information on when the app was retired (possibly useful for updating the tag wiki and/or leaving comments) and some possible alternative apps, if applicable.
Google+
Retired for consumers 2019-04-02. Still available as part of G Suite.
google-plus (open)
Should not be closed by default. If the question is specifically about the G Suite version or is applicable, it should be left open.
Alternatives: Facebook, Twitter, Instagram
Google Checkout
Replaced by Google Wallet: 2011
google-checkout (open)
Google Code
Retired: 2015-03-12
google-code (open)
Alternatives: Github, Bitbucket
Google Inbox
(See Inbox by Gmail below)
Google Instant Search
Returned search results in real time. As more than half of all Google searches are on mobile, this was deemed less than optimal.
google-instant (open)
Google Latitude
Retired: 2013-08-09
google-latitude (open)
Google Plus Photos
Being replaced by Google Photos starting 2015-08-01 (see [1] and [2])
google-plus-photos (open)
Google Reader
Retired 2013-07-01
google-reader (open)
Alternatives: The Old Reader, Feedly, Netvibes
Google Talk
Replaced by Google Hangouts, 2013-05-15
Completely removed from Gmail, 2017-06-24
google-talk (open)
Questions with this tag should not be "closed by default" as this tag is used for the Google Chat overall platform. The last remaining holdout for Google Talk, Gmail, will lose that feature for good in June, 2017. It has as synonyms:
Google Wave
Retired 2012-01-31
google-wave (open)
Gowalla
Retired 2012-03-10
gowalla (open)
Alternatives: Foursquare/Swarm
Grooveshark
Retired 2015-04-30
grooveshark (open)
Alternatives: Rdio, Google Play Music, Pandora
Hotmail
Replaced by Outlook.com, 2013
hotmail is a synonym of outlook.com
iGoogle
Retired 2013-11-01
igoogle (open)
Alternatives: igHome, NetVibes, start.me
Inbox by Gmail
Retired 2019-04-02
inbox-by-gmail (open)
Alternatives: Gmail, Outlook.com, Yahoo! Mail, many others
Meebo
Acquired by Google 2012-06-04
meebo (open)
Alternatives: IM+, Trillian
Orkut
Retired 2014-09-30
orkut (open)
Alternatives: Facebook, Diaspora
Picasa Web Albums
Shut down 2016-08-02 (source)
picasa-web-albums (open)
Alternatives: Facebook Photo Albums, Flicker, Google Photos, Instagram, etc.
Posterous
Shut down 2013-04-30
posterous (open)
Alternatives: Blogger, WordPress.com
Postini
Email, security, and archiving service folded into G Suite and discontinued in August, 2012
postini (open)
Vine
Smartphone apps discontinued October, 2016. Archive of old videos remains, but all social network aspects have been shut off.
vine (open)
Writeboard
Retired unknown; functionality folded into Basecamp
writeboard (open)
Alternatives: Basecamp
Yahoo Pipes
Retired 2015-09-30
yahoo-pipes (open)
Alternatives: IFTTT