Catching multiple types of exceptions when writing JSON I have a class which throws a lot of exceptions: 

    try {
        mapper.writeValue(outStream, myVal);
    } catch (JsonGenerationException e) {
        e.printStackTrace();
    } catch (JsonMappingException e) {
        e.printStackTrace();
    } catch (IOException e) {
        e.printStackTrace();
    }  


I think this looks messy. Is it ok to just catch a generic Exception and not catch each individual exception if within the catch clause of each exception I'm just printing the stack trace?
It is okay to just catch Exception and print the stack trace.
However rather than catching the top level Exception class, you may want to look at the Java 7 exception handling: http://docs.oracle.com/javase/7/docs/technotes/guides/language/catch-multiple.html

In your case:

try {
    mapper.writeValue(outStream, myVal);
} catch (JsonGenerationException | JsonMappingException | IOException e) {
    e.printStackTrace();
}