What sort of motor is best for continous high torque applications?
High torque - BLDC probably. Good for continuous as no commutator to wear.
Commercial BLDC + controller = expensive though - perhaps you don't mean "best"?
If very large motor needed and large budget, then superconducting motor will be
hard to beat for torque: 36.5 Megawatt superconducting motor Successfully Tested at Full Power | NextBigFuture.com 8)