One resident process that is installed alongside the JRE is the Java Updater.
The linked page also shows how to disable it:
III. Configure Java Updates
Automatic Update Feature
- Click Start > Settings > Control Panel (For Windows XP)
Click Start > Control Panel (For Windows Vista and Windows 7)
- Double-click Java icon. The Java Control Panel appears.
- Click the Update tab
- The Update tab may not be available if your network administrator has disabled the Java Update feature during installation.
- If you are not logged in to system as administrator then options to change Java update notifications will be greyed out and user will not be able to change it.
- To enable Java Update to automatically check for updates, select the Check for Updates Automatically check box.
- To disable Java Update, un-select the Check for Updates Automatically check box.
Obviously, it will also install ActiveX components and such, which might have a minor impact on overall system performance. But I don't think they should be noticeable. And if you wanted to get rid of those, then I don't think the JRE will still work.