Proper way to close an OutputStream in Java?

If you are using Apache Commons, then IOUtils.closeQuietly() does the job nicely. See http://commons.apache.org/proper/commons-io/javadocs/api-1.4/org/apache/commons/io/IOUtils.html#closeQuietly(java.io.OutputStream)

I don't think the exception should be swallowed. The caller is misled to believe that the content is written successfully. The exception should propagate upwards.

If you don't like checked exceptions (especially for such low level errors), wrap it as unchecked. Or you can follow Java's convention, for better or for worse, and declare IOException on your method.