Sometimes, particles are omitted.
I've read, however, that this can be analyzed as inserting a "zero particle" instead. See for example Particle omission or zero particle by Mitsuaki Shimojo. See also Matt's comment on a related question.
Are there situations where a zero particle is required? That is, situations where adding any particle would change the meaning or make the sentence incorrect?
Are there situations where a zero particle is strongly preferred?