Come March 2017 with the release of JDK 9, Oracle's Java Web Plugin will be deprecated, Oracle announced on their blog. Other companies have been working on killing the plugin for a while. Microsoft's Edge was shipped without support for it, Chrome recently removed support, and Mozilla has plans to remove both Silverlight and Java support by the end of 2016.
The plugin began life as a way to introduce app-like features to web pages, but over time, the sheer number of security flaws frustrated so many users and IT departments that it's reputation fell in the toilet. In 2013, it was responsible for 91% of all computer attacks. Heimdal Security has an interesting report on several of the security vulnerabilities as well.
In 2009, I was infected with the Vundo/Virtumonde virus (and rootkits!) that installed fake malware detection software and redirected web page I tried to open to an advertisement. The most common way to get this virus? Issues with not updating the Java plugin frequently enough. I'm not too choked up about this news.
So by 2017, your computer will stop asking if you want to install the latest Java plugin, and instead move to Oracle's new Java Web Start for launching in-browser Java applications.
For more information, you can find Oracle's official blog post here.