Now that the ESA has landed a probe on a comet, namely Rosetta's Philae Probe, could we possibly land a probe on Halley's comet? Fuel seems to be a limiting factor for interstellar expeditions - could using Halley's comet as a free taxi, shutting down all equipment once landed to save fuel and energy, aid in such expeditions?
There seems to be a fundamental misunderstanding as to how movement in space works. In space there is no air friction, that is, once you are moving toward your destination, you don't need a continuous source of power to keep going. Landing on a comet doesn't buy you anything, since in order to land you must first match the comet's orbit, at which point the comet could disappear and you could still shut down your engines and follow the exact same path it would have taken you.
As @ChrisWhite has already stated, catching up with Halley's comet offers no appreciable benefit since you'd already need to be traveling at the same speed in a frictionless environment.
Where you could get a big boost is if your probe was positioned in the comet's path, either coming across it at an oblique angle or simply stationary, relative to the comet.
Assuming unbreakable meta-materials are available to you, you could then use a harpoon to grab onto it, or simply allow it to hit your probe, transferring a very sizeable amount of kinetic energy to your device.
Conservation of energy means that it would take you just as much energy to catch up with the comet and make a soft landing (in the ideal case where you ignore the extra fuel costs for landing) as you would need to launch the spacecraft in a similar orbit as the comet. What you could do is let the comet give a bounce to the spacecraft, but I don't think this is technically feasible, you'll end up smashing the spacecraft to pieces.
As earlier answers have stated this method doesn't work to save fuel directly, however it might still be useful to hitch a ride on a comet using it for a gravitational assist that the probe would not survive without more shielding than is practical. Placing the body of the comet between the Sun and the probe would presumably shield it from much of the solar radiation and heating that would be experienced.
Therefore whilst not directly saving fuel this might allow the use of more direct flight paths so, were the comet not used, the probe would require the use of additional fuel to reach the same end point safely in the same duration.
Fuel, or better energy indeed is the limiting factor. You can steal energy using a gravity assist, but comets simply don't have enough gravity. Jupiter is much more massive, and a gravity assist around Jupiter would in fact make sense for an interstellar probe.
Still, it's only a single boost as you fly by Jupiter, and you have to spend the fuel to reach Jupiter's orbit.