Some motors require DC to make them work and the direction they turn is determined by which way round you connect the supply AC will just make them vibrate backwards and forwards at the mains frequency. If they have a permanent magnet in them, then this is the case and you need a power supply off the mains or a battery to work them. Most of the motors in mains operated hand tools etc. use an electromagnet, which uses the mains supply too. The motor will go in the same direction, irrespective of the instantaneous polarity of the mains waveform and many of them will also work on DC. It is true to say that the torque on a normal AC 'Brush Motor' does vary in time (as you suggest) - partly because of the AC variation but also because of the angle of the armature coil as it turns. But they are usually made with 'multiple poles' which smooths out these pulses so they do not affect the operation.
There is a third type of motor - and Induction Motor, which requires an AC supply for it to work. Pretty much all really big motors are Induction Motors because they are very efficient and many Induction Motors work off a Three Phase mains supply and they have constant torque throughout the cycle.