Let?s clarify the language here. Two conductors are in parallel if, and only if, they are joined at both ends. As ptonsparky mentioned, you can use parallel conductors to increase the ampacity of feeders and services. 310.10(H) has the applicable rules. One of the rules would prohibit paralleling the neutral (or ungrounded) conductors for most of the branch circuits we commonly deal with. The minimum size for paralleling conductors is 1/0, and most of my branch circuits use #12 or #10.
Different from this situation is using a single neutral wire to serve as the return path for more than one branch circuit. I think this is what ptonsparky and GoldDigger described. That is allowed only under very specific conditions that are described in 210.4. If the two branch circuits originate from different phases of the same panelboard, and if their breakers have listed handle ties (or are multiple-pole breakers), then perhaps this creates a legal ?multi-wire branch circuit.? If the two branch circuits originate from the same phase, or originate from different panelboards, or do not have common trip capability, then this is illegal and unsafe.
Now, having said all that, please tell me whether you are talking about a parallel situation, or about a MWBC situation, or about something else.