How to handle unused wire in cable
If you already have a ground connection with one or more other wires, then use the otherwise unused wires to make a more solid ground connection.
If there is otherwise no ground connect, like with ethernet for example, then I agree with Keelan in that you shouldn't create one. That could cause trouble with ground loops. In that case, either leave the extra line floating or connect it to ground at one end only.
In your particular example, the extra wire should be connected to the chassis ground of the meter and unconnected at the sensor. Since the wire is acting as an antenna, this gives any noise that is picked up a place to go that will not interfere with your signals.
In general, it depends on the design of the system. What is the extra conductor? Single wire, multiple wires, a wire and a shield, multiple shields? Are there power supplies at both ends? Are they isolated? Are the other conductors signals from a sensor (as in your example) or communication over a network?
This answer by Kortuk and the comments that follow make some really good points.
And this short article describes the advantages and disadvantages of various connection schemes:
For cable shield connections there are four options, with advantages and disadvantages:
Shield grounded at both ends: Good r.f. shielding but susceptible to ground loop currents that can be VERY large - up to at least 100 A in bad cases.
Shield grounded at both end, with large-area parallel bonding wire: Good at r.f. and now the ground current flows mainly through the bonding wire, but the intense magnetic field that may result is not good news. The bonding wire size needs to be, for example, 10 mm^2.
Shield grounded at one end only: No ground current but not good at radio frequencies for which the cable is more than 1/8 wavelength long. R.F. interference may actually be worse than for an unshielded cable.
Shield grounded at the sending end and grounded through a capacitor (may be two in parallel, for effectiveness from about 100 kHz up to 1 GHz and beyond) at the receiving end: Good at r.f. if the capacitor type and positioning are correctly-designed, and no low-frequency ground current. One capacitor needs to be of the type with an integral spark- gap so that it is not damaged by transient high-voltage spikes that may be induced on to the shield.
I believe Olin nailed the best solution here: double up the ground for a more solid ground, since there already is a ground, and it looks like it carries return current from the +12V that powers the sensor.
I don't agree with the idea of grounding the wire on one end of the cable. Grounding the unused wire on one end could be detrimental, particularly if none of the existing wires are ground (there is a return current, of course, but suppose it's not ground). Adding a ground wire just creates a parasitic capacitive path to ground all along the length of the cable! This could be bad even if one of the wires is already ground. There is already capacitance between a signal wire and the existing ground wire. Another ground in proximity only increases the capacitance: and since it is connected on one end, it does not decrease the resistance! Thus the RC product goes up.
Lastly, grounding on one end is a good practice only for cable shields. Not for inner conductors! The ground of a cable shield should be conducted directly to a star point in the power supply of the device to which it is connected, so that noises from the cable shield bypass the circuit board. If the cable shield ground goes through the circuit board, you have potentially created a "pin 1 problem"
Speaking of which, something to consider is whether the cable has an external shield: is this extra wire shielded? If there is no shield, then by connecting this unshielded wire to either device on either end of the cable, you're basically adding an antenna which brings noise into that device. That wire's action of picking up noise does not help the other wires in any way, because it is not a shield that is wrapped around the other wires.
So in the best case (there is a good cable shield), you're adding a capacitive frequency-response-sucker. In the worst case, you're adding a noise-gathering antenna.
Our first instinct should be to leave it floating. From this default starting point, we can think rationally about how to put it to use based on the situation, which leads us to Olin's answer: make a better ground. Or perhaps reinforce some other signal.
If you're going to ground it, ground it on both ends.
Now if the cable is being used for a high impedance connection, where the return current flowing through ground is tiny, I wouldn't double up the ground. The reason is that if there is high impedance on either end, or both, it swamps the cable resistance R. We gain nothing by cutting the resistance in half. But we lose something if the capacitance goes up! The RC we are worried about consists of the C from the cable, and the big R from the circuit, not the insignificant R from the cable.
For instance, look at coax cables that are used for single-ended audio. The ground is carried in the external shield. But between the shield and the inner conductor, there is quite a bit of space, which helps to lowers the capacitance. If we add a second conductor to the inner core and use it as another ground, we now have a ground that is in a lot closer proximity to the signal. How does that help us? Capacitors get bigger with closer spacing (stronger electric field).