Update: Java version 7 updates 10 and above add additional security settings. If you have programs that require Java to work, you'll want to read how these settings can make you safer.
Security researchers recently discovered two gigantic security flaws in Java version 7 that allow hackers to silently take control of both PCs and Macs. In the few days since this discovery, more than 100 malicious websites have appeared that exploit these flaws.
Oracle, the developer released a patch, but that contains some flaws as well.
Unless you really need Java, you should remove it.
In Windows, go to Start>>Control Panel and click the Uninstall a program link. Find Java on the list of programs. If you have version 7, uninstall it.
Note: Java version 6 is not affected by this issue, but it is an older version with its own problems, so you might want to uninstall it anyway.
In OS X 10.7 and 10.8, go to Macintosh HD/Library/Java/JavaVirtualMachines/ and remove the 1.7.0.jdk file. Older versions of OS X run Java 6.