Should one call .close() on HttpServletResponse.getOutputStream()/.getWriter()?
Normally you should not close the stream. The servlet container will automatically close the stream after the servlet is finished running as part of the servlet request life-cycle.
For instance, if you closed the stream it would not be available if you implemented a Filter.
Having said all that, if you do close it nothing bad will happen as long as you don't try to use it again.
EDIT: another filter link
EDIT2: adrian.tarau is correct in that if you want to alter the response after the servlet has done its thing you should create a wrapper extending HttpServletResponseWrapper and buffer the output. This is to keep the output from going directly to the client but also allows you to protect if the servlet closes the stream, as per this excerpt (emphasis mine):
A filter that modifies a response must usually capture the response before it is returned to the client. The way to do this is to pass the servlet that generates the response a stand-in stream. The stand-in stream prevents the servlet from closing the original response stream when it completes and allows the filter to modify the servlet's response.
One can infer from that official Sun article that closing the OutputStream from a servlet is something that is a normal occurrence, but is not mandatory.
The general rule of them is this: if you opened the stream, then you should close it. If you didn't, you shouldn't. Make sure the code is symmetric.
In the case of HttpServletResponse, it's a bit less clear cut, since it's not obvious if calling getOutputStream() is an operation that opens the stream. The Javadoc just says that it "Returns a ServletOutputStream"; similarly for getWriter(). Either way, what is clear is that HttpServletResponse "owns" the stream/writer, and it (or the container) is responsible for closing it again.
So to answer your question - no, you should not close the stream in this case. The container must do that, and if you get in there before it, you risk introducing subtle bugs in your application.
If there is any chance the filter might be called on an 'included' resource, you should definitely not close the stream. This will cause the including resource to fail with a 'stream closed' exception.