The Differential Sail is probably the simplest form of space drive, and uses Cosmic Background Radiation and/or vacuum fluctuations as its source of varying energy to create a pressure gradient in space. A Differential Sail would act like a radiometer vane, generating a net difference in radiation pressure exerted across the reflecting and absorbing sides, similar to a Solar Sail that utilizes the entire freakin' universe as its radiation source rather than one puny star or laser.

In addition to being the simplest space drive, the Differential Sail is also likely to be the slowest space drive, although it would not require the vehicle to expend any more energy than is required to turn the Sail in the right direction. Also, the Differential Sail is one of very few space drives that do not exert a force on all particles of a vehicle simultaneously, meaning that the crew would experience the effects of acceleration; this is unlikely to be much of an issue, however, as acceleration would be very slow.

The Diode Sail is an ideal Differential Sail that allows space radiation to pass through from one direction (resulting in zero net force from that direction) and reflect from the other like an ideal one-way mirror or diode.

tdent asks: I don't see how this can work. The microwave background is isotropic to a very good approximation - i.e. the same in every direction. How can you convert that into a net force?

Actually, this is a good thing. Isotropy is necessary to make this a good space drive. If the microwave background radiation was anisotropic, it would be much easier to accelerate in certain directions and harder to accelerate in others.

For any of these concepts to work, there must be a real background medium in space. This medium must have a sufficiently large energy or mass density, must exist equally and isotropically across all space, and there must be a controllable means to alter the collisions with this medium to propel the vehicle. A high energy or mass density is required to provide sufficient radiation pressure or reaction momentum within a reasonable sail area. The requirement that the medium exist equally and isotropically across all space is to ensure that the propulsion device will work anywhere and in any direction in space. The requirement that there must be a controllable means to alter the collisions ensures that a controllable propulsive effect can be created.

We already have the isotropic medium (most likely Cosmic Background Radiation, but Zero Point Fluctuations or free hydrogen might be made to work as well). What we need, then, is a way to alter the collisions with the medium. And, lo and behold, that's easily available: as we all know from reading far too much sci-fi, solar sails are reflective because bouncing the photons back where they came from exerts more radiation pressure than simply absorbing them. So, if you make one side of your sail reflective, and the other absorbtive, (or transparent in one direction, if you can manage it), the reflective side will experience a larger pressure than the absorbtive side, resulting in a net force on the vehicle.

Black-backed solar sails, however, while doable with current technology, do have some problems. As already noted, a differential sail is not likely to accelerate very fast. And, as pointed out in unperson's excellent WU below, if we track where the energy is coming from to move the sail, we find out that it won't be able to accelerate indefinitely either. So, let's have a closer look at implementing a differential sail:
If you have a perfect one-way mirror (that is, some substance which is perfectly transparent to light in one direction, and perfectly reflective in the other), it is easy to see that all of the light pressure exerted on the sail will be on the reflective side. As the sail accelerates, the Dopler effect will cause light leaving it to be less energetic than the light hitting it, with the excess energy going into accelerating the sail. This has the net effect of cooling the universe, converting the roughly-uniform ambient heat into the kinetic energy of the sail. Unfortunately, this violates the 2nd law of thermodynamics, so, barring a major revolution in physics, it is safe to assume that such a material is not possible. unperson has expressed dismay that this fact could excape mention on a NASA website, but one must take into account that the website in question* is part of NASA's Breakthrough Propulsion Physics Program, of which one of the major assumptions is that a major revolution in physics will be required for most of the ideas to work.
If you have a black-backed solar sail (that is, a substance which is perfectly reflective on one side and perfectly absorbtive on the other, more specifically called a diode sail), the situation is similar to that above, except that the radiation pressure on the reflective side is counteracted by the emission of blackbody radiation from the absorbtive side. Therefore, if the sail is kept cooler than the medium in which it is working (here assumed to be the Cosmic Microwave Background), it will act as a heat engine, transforming the temperature difference between itself (the cold reservoir) and the universe (the warm reservoir) into the kinetic energy of the sail. The acceleration of sail decreases with the temperature difference, and no thrust is provided when the sail reaches thermal equilibrium. Actively cooling the sail (if we are not going to violate thermodynamics) requires the expenditure of extra energy, presumably provided by some on-board source, and requires radiating the excess heat away. One would want to radiate waste heat so as to provide thrust in the same direction as the reflective side of the sail, and in this way we have just derived the photon rocket. Now, the heat engine is running in reverse, with the sail acting as the warm reservoir and the universe acting as the cold reservoir, and converting the temperature difference into the kinetic energy of the sail.
Sails working in other mediums (like quantum fluctuations, for example) can generally be analyzed in the same way. A Gravitophoton Field Propulsion engine, for example, would behave like a diode sail working in vacuum fluctuations, preferentially absorbing particles which exert a force in the desired direction of thrust and allowing others to pass through.

To illustrate: (Standard Differential Sail) (Diode Sail) *Information on space drives: