web browsers that support java
Lobo is an extensible all-Java web browser and RIA platform. It supports HTML 4, Javascript (AJAX) and CSS 2 plus direct JavaFX and Java (Swing/AWT) rendering. Cobra is the web browser's renderer API; also a Javascript-aware HTML parser.
Use IE Tab for Chrome. The best way to use Java (or Silverlight, or other NPAPI-based technologies) going forward is to use IE Tab for Chrome. You can set up Auto URLs to automatically open certain urls using IE Tab, providing a seamless experience, as if Java support never went away. Get it here: