Using the CrmService, there are a number of SetStatus methods for the built-in entities.
For Incident, you would use SetStateIncident like this:
CrmService service = new CrmService();
SetStateIncidentRequest request = new SetStateIncidentRequest();
request.IncidentState = IncidentState.Active;
request.IncidentStatus = -1;
request.EntityId = <YOUR GUID HERE>;
SetStateIncidentResponse response = (SetStateIncidentResponse)service.Execute(request);
This code can be used in a plug-in, or other application (e.g. console app).