This number defines absolute lack of 'substance', nothingness, emptiness and is usually associated with a negative significance. Consequently, as a dream symbol it may stand for something you lack in the waking life (a certain object, feeling, state of mind etc.), for your flaws of character, for a major loss you have experienced recently etc.
If we consider zero as also representing timelessness, then it may bear a positive dream significance by illustrating lack of boundaries, absolute freedom, eternity etc. In this light, zero in dreams may be interpreted as a symbol of your independent and ambitious nature or announcing 'bright horizons' to be soon seen by you in the waking life.
Digit zero as dream symbol may also be a metaphor for the 'zero hour', illustrating the initial phase of a project, undertaking etc. Consequently, it predicts taking up new actions, entering a new business etc. which may turn out to be a complete success and bring prosperity into your life.
But the number zero may also represent unworthiness - low self-esteem or your opinion that a person you know has zero value, therefore is unworthy.