Systematically, what would happen if I give a crank at the shaft of a motor?
The thing that you will do is to induce an EMF in the motors, which is plainly said a voltage.

For inducing an EMF you will need one thing: changing magnetic flux. So if it has absolutely no magnetization(which changes because of rotation) it won't work. This initial magnetization(for PM-less machines) can be brought in by inputting some DC, or unsymmetric AC. This way you get a magnetic axis, which isn't in the same place as your torque producing axis. With a cross product of the magnetic and torque producing axis you will get some force and torque, therefore they may not be the same.

Brushed motors

The brushed motors can have different excitations. We assume that the load is a resistor. Now let's take a look at the subtypes:


PM excitation: It will produce a DC voltage that is proportional to the speed. The torque-rpm graph is linear.
Parallel/Serial excitation: There needs to be some remaining magnetization in it, otherwise it is just some iron and copper. Assuming that it has this little magnetization you will get increase in current gradually, as it magnetizes itself. After some time it will stabilize. The speed will factor into the excitation and into the armature voltage. It can be calculated though, as the equations aren't complex. Parallel and serial will come to the same thing in this constellation.
Compound excitation: Will come to the same as parallel/serial, it will have a more complex model though.


AC-Machines

For three phase machines it will be assumed that 3 resistors are connected either in delta or wye, unless stated otherwise.


PM excited synchronous machine - It will work without problems, it will give 3-phase AC. The voltage and the frequency will be dependent on the rotational speed.
Reluctance synchronous machine - This one works with a magnetically asymmetric rotor/stator instead of having permanent magnets. It requires some remaining magnetization as said earlier. You should connect some capacitors on the load side as to give some phase shift to it, that way you will create phase shifted magnetization current. Based on this principle it could work fine.
AC Induction motor - This case will be similar to the reluctance synchronous machine. Capacitors and some remaining magnetization required.
BLDC Motor - basically the same as a PM excited synchronous. The difference lies in the output EMF, it will be trapezoidal instead of sinus like.
Single phase - Ask in the comments if you want them.
Electrically excited - Those are actually used in power stations, you need some current though for the magnetization. This DC excitation current can be created easily, but you need some additional equipment.


None of them will go into smoke except if you short them and crank to hard, but for this you need a large rotational speed. The power you put in through the crank will be used on the load(and in some cases for remagnetizing). Therefore even with a 100W bulb as load, you will be hard pressed to make it light up(as a normal human).