Motor acting as a generator with backfeed

The force that causes motion is due to the interaction of two magnetic fields, at least one of which is created by a current flowing through a conductor. Force is given by F=BIL, which is, essentially, the Lorentz force.

In a generator, a voltage (and consequent current if there's a circuit) is created by moving a conductor in a magnetic field. Mechanical energy is thereby converted to electrical energy (if a current flows). If there is no circuit, there will be zero current, and zero force is required to move the conductor. The induced voltage (actually, an EMF) is E=BLv, where v is the velocity of the conductor wrt the magnetic field.

A HDD motor usually is brushless, i.e. it has no commutator. Basically, it consists of three coils arranged around a magnetic rotor. There are three terminals to power the three coils and one common current return terminal:

You can drive the motor by a 3-phase AC voltage, and when you turn it by hand, it will generate a 3-phase AC voltage.

Here is a youtube video of someone who measured the voltage on all three terminals while spinning the motor by hand. This screenshot from the video shows a wonderful 3 phase voltage:

As you need DC, you could use three rectifiers:

^{simulate this circuit – Schematic created using CircuitLab}

or six diodes, as @jms pointed out:

^{simulate this circuit}

However, I'm not sure how powerful those motors are, or how much power you get out when using them as generator. @JRE's experience (see comment) is that the power is very low. This may not be enough for your experiments, but if you want to try, choose diodes/rectifiers with low voltage drop (schottky diodes) to reduce the losses in them.