Generally speaking, under part 91, published ODP's are optional, ATC assigned departures (including headings) aren't. But under 121 or 135 there may be company policies that come into play. My previous company had guidance in their FOM for IFR departures that were generally more restrictive than the FAR/AIM - basically, if we weren't assigned a named SID or given a departure heading (like from an uncontrolled field) then we had to fly the ODP regardless of the current wx conditions.