Is it common for jets not to have backup manual control system for emergencies?
On any large jet (the DC-10 was a wide-bodied plane, seating around 300 people), the control surfaces are simply too large to move without hydraulics. Manual control is impossible, and multiple redundant hydraulic systems are provided. This applies to any large plane.

It's considered unlikely that all the hydraulic systems will fail independently. The specific problem on United flight 232 was that the failures weren't independent: all three hydraulic systems were severed by the engine in the tailplane failing and spewing lumps of metal into the narrow conduit that carried the hydraulic lines.