To suppress serializing properties with null values using Jackson >2.0, you can configure the ObjectMapper directly, or make use of the @JsonInclude annotation:

mapper.setSerializationInclusion(Include.NON_NULL);

or:

@JsonInclude(Include.NON_NULL)
class Foo
{
  String bar;
}

Alternatively, you could use @JsonInclude in a getter so that the attribute would be shown if the value is not null.

A more complete example is available in my answer to How to prevent null values inside a Map and null fields inside a bean from getting serialized through Jackson.

Add JsonInclude to relevant classes Response and Data

(updated using @ThomasFritsch comment)

@JsonInclude(JsonInclude.Include.ALWAYS)

Value that indicates that property is to be always included, independent of value of the property.

i would suggest to simply make a null check, or as you sugested, handle via exception.

@Override
    public void serialize(
      Prodotto prod, JsonGenerator jgen, SerializerProvider serializer) throws IOException {
        jgen.writeStartObject();

//      getPeso_netto returns an Integer, that in the example is null
        if (prod.getPeso_netto() != null)
            jgen.writeNumberField("peso_netto", prod.getPeso_netto());
        else {
            jgen.writeNullField("peso_netto");     
        }

EDIT Explanation

the method JsonGenerator.writeNumberField has following method body:

public final void writeNumberField(String fieldName, int value) throws IOException {
    this.writeFieldName(fieldName);
    this.writeNumber(value);
}

as you see, the method is expecting an int, not an Integer. The compiler is trying to Autobox the Integer to an int. This fails with an NPE, because the Integer is a null object. So the NPE is not thrown 'by code of jackson library', but from the JVM at the point trying to pass an autoboxed null value as an int to a jackson method.

You can test this behaviour with following snippet:

Integer x = null;
x = 1 + x; // will throw NPE

You have the annotation in the wrong place - it needs to be on the class, not the field. i.e:

@JsonInclude(Include.NON_NULL) //or Include.NON_EMPTY, if that fits your use case 
public static class Request {
  // ...
}

As noted in comments, in versions below 2.x the syntax for this annotation is:

@JsonSerialize(include = JsonSerialize.Inclusion.NON_NULL) // or JsonSerialize.Inclusion.NON_EMPTY

The other option is to configure the ObjectMapper directly, simply by calling mapper.setSerializationInclusion(Include.NON_NULL);

(for the record, I think the popularity of this answer is an indication that this annotation should be applicable on a field-by-field basis, @fasterxml)

You need to configure your object like this: mapper.setDefaultPropertyInclusion(JsonInclude.Include.ALWAYS);