The short answer is no, this is a practical impossibility, but not only because of the earth's magnetic field per se; it's because of the Earth's gravity. Let me break this question down into a few key areas to discuss the matter in detail;
Gravity creates Friction
The reason why wheels are so efficient in terms of propulsion is that they get an assist from gravity. The weight of a car (for example) pushes the tyres down onto the road, resulting in tension, which results in friction. The reason why we use a rubber tyre and grease around the axle is that we want to minimise the friction between the axle and its casing and transfer all the angular force to the wheel. The rubber on the tyre creates so much friction that the only way the angular force can apply is for the wheel to roll rather than spin. This converts the angular force to forward force, pushing the vehicle forward.
This means that the car uses the energy it creates very efficiently to move from its current position to where you want it to go, and gravity is actually helping this rather than the enemy. This is also why cars spin their wheels when bogged in slippery mud or when the energy being applied to the wheels overwhelms the friction applied by the tyre. This in essence reflects the whole debate around power to weight ratio in cars, and also explains why many professional racing cars have such wide tyres (to maximise friction).
But (I hear you say) that only benefits lateral movement, right? It's not true for rising above the earth's surface, right?
Wrong. This is the whole debate around space elevators. Right now, we use rockets to get things out of the Earth's gravitational pull. The problem with that is that the gravitational pull is constant, meaning that thanks to something called the rocket equation, you need massive amounts of fuel to get your payload into space because you don't only have to lift your payload, but the fuel to lift it as well. On the other hand, by gripping some form of very tall, super strong rope tightly, you can use friction to climb out of the gravity well. If you use a counterweight on your elevator car, you can even do so with minimal energy cost for the climb. Either way, if we had the right material science advancements, space elevators can use friction to get stuff out of the gravity well at a far lower cost than getting it to 'float' upwards at a great rate of knots.
Orientation & Lateral Movement
As has already been discussed in the compass example, magnetic fields are good for alignment. That is to say, if you already have something floating freely, the earth's magnetic field will automatically align the magnet to said magnetic field. This means that to steer, you literally need to dynamically adjust the alignment of your magnetic polarity to the direction you want to go. This could be done through friction as well, using a de facto steering wheel to turn a strong magnet under your vehicle, so that fixed thrusters can move you along.
This of course brings us to sunny point number 2 - lateral movement. You still need some way to get your vehicle moving in a given direction, without contact to the ground. On an aircraft or hovercraft, this is usually done with a fan style thruster. Even most modern jet engines are really turbofan engines, capable of great amounts of thrust by pushing air backwards very fast.
It's also why you can't use a hoverboard over water, as we all learned in Back to the Future II. This is not exactly true of course; if you had an oar, you could move along very quickly because the oar maximises the friction between itself and the water, and with NO friction on the hoverboard and the water, in theory you move forward. I say in theory because in a strong headwind, you might be fighting a losing battle with forward movement. But, I digress.
Magnetic Intensity over Distance
Maglev trains (for example) can float a train above the magnetic rail because the magnets are strong, and they're also close together. The earth's magnetic field is strong to be sure, but we're actually reasonably far away from the 'magnet', being the inner core of the Earth. The intensity of the magnetic field at distance is inversely proportional to the square of the distance, meaning that the intensity reduces greatly the further you move away from it. That means to get that same train to float off the track, you need magnets in it that are so intense they can counteract gravity against the earth's inner core, rather than the earth's surface. If you design such a magnetic field, you could use it to melt pidgeons or exsanguinate cows by ripping the haemoglobin directly out them if they stray close enough.
Bottom line is you're better with two magnets interacting in close proximity to maximise the efficiency of your levitation.
We have to assume here that you're using electromagnets to do all this. Given that gravity is always on, so too do the electromagnets have to be. If they aren't, your vehicle fails badly by collapsing back to the ground. Your electromagnets have to constantly expend energy to counteract gravity.
A car on the other hand simply stops. This is because it's spending all its energy moving forward, not counteracting gravity. Not having to do that, actually using gravity to maximise friction, makes a wheel based vehicle a far more efficient user of kinetic energy than a magnetically levitating vehicle for that reason alone, but it also means that it is by far the safest solution in terms of what happens during an engineering or power failure.
Mark Twain once said 'Thunder is loud. Thunder is impressive. But it's lightning that does all the real work.' Well, mag-lev transportation looks very impressive to be sure but it's friction that is going to do all the real work in terms of transport systems in a real world application. Wheels may sound very 'old tech' but the reason we're still using them is they are still the best and most efficient energy solution for moving people and stuff around. The biggest problems that you have with the model you describe are that you're constantly fighting gravity by reacting to a distant magnet, and you still need mechanisms to propel yourself through the air laterally if you get your craft floating.
Star wars may have worked very hard to make the wheel look unfashionable, but I'm still of the view that it's a very impressive tool.