As of this writing (2017-05-16), the situation is in flux. Items:

• The historical closed-source uberstandard for both Java virtual machine and plugin, this being Oracle (originally Sun), is supporting plugins for its current version, 8, but has announced a ceasing of plugin support for 9.
• The open-source plugin standard, IcedTea, shows no signs of weakening, and works very well indeed with both Oracle’s Java and the open-source OpenJVM and others as well. However, no Windows porting is known to this author.
• Firefox and Chrome do not support Java in their current versions. There is an Extended Support Release version of Firefox which does, for a little while longer.
• Pale Moon, a very distinctive Mozilla/Firefox variant, is reported to support Java.
• Opera is reported to support the Oracle/Sun JVM only.
• Midori is reported to support both Oracle’s and IcedTea.

The author is working on practical tests of the last three.