With regards to FAA part 121 ops, If no TAF is available, we would use the Area Forecast for the geographical area of the airport in question to determine whether we can initiate the flight or not. With regards to METARs (to include other official weather such as ASOS info, etc.), an unfavorable METAR would prevent the flight from dispatching if the METAR would still be valid at the ETA.
Example for dispatch minimums: TAF forecasts MVFR conditions all day long. Our flight is 20 minutes long. Current METAR for destination airport, which will still be valid at our ETA, shows below mins conditions. Though the forecast is good, the METAR prevents us from departing. If the flight was longer and would put us on the ground after the next METAR change, then the forecast would become the controlling item. If the METAR trend for the last few hours has shown something markedly worse than forecast for a consistent period of time, then it would also be something to consider if the arrival time was still relatively soon. Obviously for a much longer flight the current METAR would be more or less irrelevant at our ETA, so would typically not be a consideration in normal situations.
It does not work both ways; e.g. on the same 20 minute flight our TAF forecasts zero-zero but the METAR (which will still be current at ETA) shows VFR, we still cannot begin the flight until the forecast changes.
Basically take all reports (METARs, AWOS reports over the phone, etc.) and forecasts (TAFs, or if not available Area Forecasts) that will be valid at your ETA, and the WORST one becomes controlling for dispatching the flight.