As toolkit mentions above, Apache Commons IO is the way to go, specifically FileUtils.copyFile(); it handles all the heavy lifting for you.
And as a postscript, note that recent versions of FileUtils (such as the 2.0.1 release) have added the use of NIO for copying files; NIO can significantly increase file-copying performance, in a large part because the NIO routines defer copying directly to the OS/filesystem rather than handle it by reading and writing bytes through the Java layer. So if you're looking for performance, it might be worth checking that you are using a recent version of FileUtils.