B737-300
Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 174; Flight Crew Type 174
Aircraft Equipment Problem Critical
General Declared Emergency
Aircraft
We were at cruise FL340 when the Cabin Pressurization Warning sounded. We donned our masks and initiated an emergency descent. Cabin altitude showed 12;000 feet and slowly climbing. We completed QRH procedures while descending. During descent the passenger emergency oxygen system activated and I was informed by the flight attendants that the masks had dropped. At 10;000 feet I had the flight attendants check the passengers for medical stress and/or difficulties. My decision [to continue to destination] was based on the [lack of] passenger [distress] and fuel status. Had we been low on fuel or if we had a passenger in distress; we would have landed [short]. Since there were no passenger issues and we had adequate fuel; I elected to continue to original destination. Landing was uneventful and deplaning was normal. There was a concern about the odd odor we noted when we removed our masks at 10;000 feet. Neither the First Officer nor I recognized it. I asked the flight attendants the cabin status and the A told me that the odor and mist were from the passenger oxygen generators.
B737-300 Captain experiences a loss of cabin pressurization at FL340. Oxygen masks are donned and QRH procedures are complied with during descent.  After leveling at 10;000 feet and after considering passenger distress and fuel status; the crew elects to continue to destination.