throws Exception in finally blocks

I typically use one of the closeQuietly methods in org.apache.commons.io.IOUtils:

public static void closeQuietly(OutputStream output) {
    try {
        if (output != null) {
            output.close();
        }
    } catch (IOException ioe) {
        // ignore
    }
}

If you're using Java 7, and resource implements AutoClosable, you can do this (using InputStream as an example):

try (InputStream resource = getInputStream()) {
  // Use the resource.
}
catch( Exception ex ) {
  // Problem with the resource.
}

I usually do it like this:

try {
  // Use the resource.
} catch( Exception ex ) {
  // Problem with the resource.
} finally {
  // Put away the resource.
  closeQuietly( resource );
}

Elsewhere:

protected void closeQuietly( Resource resource ) {
  try {
    if (resource != null) {
      resource.close();
    }
  } catch( Exception ex ) {
    log( "Exception during Resource.close()", ex );
  }
}