Removing Java will not cause any issues with your computer. You may not be able to play some online games or access/use those web sites which require it. If the computer is part of a business network, some applications may not work correctly.
Java allows you to play online games, chat with people around the world, calculate your mortgage interest, and view images in 3D, just to name a few. It's also integral to the intranet applications and other e-business solutions that are the foundation of corporate computing.
What is Java
Java is a programming language and computing platform first released by Sun Microsystems in 1995. There are lots of applications and websites that will not work unless you have Java installed...
What is Java technology and why do I need it?
If you're going to use Java, many security researchers and computer security organizations caution users to limit their usage and to disable Java Plug-ins or add-ons in your browsers.
If you need Java for a specific Web site, consider adopting a two-browser approach. If you normally browse the Web with Firefox, for example, consider disabling the Java plugin in Firefox, and then using an alternative browser (Chrome, IE9, Safari, etc.) with Java enabled to browse only the site(s) that require(s) it.
Krebs On Security: ...Java
To defend against this and future Java vulnerabilities, consider disabling Java in web browsers until adequate updates are available. As with any software, unnecessary features should be disabled or removed as appropriate for your environment.
US CERT: Disable Java in web browsers