In Firefox, select "Tools" from the main menu, then "Add-ons," then click the "Disable" button next to any Java plug-ins.
In Safari, click "Safari" in the main menu bar, then "Preferences," then select the "Security" tab and uncheck the button next to "Enable Java."
In Google Chrome, type "Chrome://Plugins" in your browser's address bar, then click the "Disable" button below any Java plug-ins.
If you're an Internet Explorer user, the process is a bit more complex. The blog Krebs on Security summarizes a procedure that "may or may not work." Alternatively, you could uninstall Java from your system, provided you don't need it for some particular application or website that's important to you.
For those who can't live without Java, Wisniewski's blog post at Naked Security offers a few other suggestions.
One final point: This flaw does not appear to affect the previous version of Java (Version 6, aka 1.6), which is the default on most Macs. So while Mac users are theoretically as vulnerable as Windows users, only those who have specifically installed Java 1.7 should be at risk.