The two major conclusions from the KISS study are: 1) that it appears feasible to identify, capture and return an entire ~7-m diameter, ~500,000-kg near-Earth asteroid to a high lunar orbit using technology that is or could be available in this decade, and 2) that such an endeavor may be essential technically and programmatically for the success of both near-term and long-term human exploration beyond low-Earth orbit. One of the key challenges – the discovery and characterization of a sufficiently large number of small asteroids of the right type, size, spin state and orbital characteristics – could be addressed by a low-cost, ground-based observation campaign identified in the study. To be an attractive target for return the asteroid must be a C-type approximately 7 m in diameter, have a synodic period of approximately 10 years, and require a ∆V for return of less than ~200 m/s. Implementation of the observation campaign could enable the discovery of a few thousand small asteroids per year and the characterization of a fraction of these resulting in a likelihood of finding about five good targets per year that meet the criteria for return.

Proof-of-concept trajectory analysis based on asteroid 2008 HU4 (which is approximately the right size, but of an unknown spectral type) suggest that a robotic spacecraft with a 40-kW solar electric propulsion system could return this asteroid to a high-lunar orbit in a total flight time of 6 to 10 years assuming the asteroid has a mass in the range of 250,000 to 1,000,000 kg (with the shorter flight times corresponding to the lower asteroid mass). Significantly, these proof-of-concept trajectories baseline a single Atlas V-class launch to low-Earth orbit.

The study also considered an alternative concept in which the spacecraft picks up a ~7-m diameter rock from the surface of a much larger asteroid (> 100-m diameter). The advantage of this approach is that asteroids 100-m in diameter or greater are much easier to discover and characterize. This advantage is somewhat offset by the added complexity of trying to pick up a large 7-m diameter rock from the surface, and the fact that there are far fewer 100-m class NEAs than smaller ones making it more difficult to find ones with the desired orbital characteristics. This mission approach would seek to return approximately the same mass of asteroid material – of order 500,000 kg – as the approach that returns an entire small NEA.
(Asteroid Retrieval Feasibility Study)

Update: See also this material on the AsterAnts: A Concept for Large-Scale Meteoroid Return and Processing, a proposal that dates from the late 1990's. (Thanks to Ashley for pointing this one out.) End update.

Robert Heinlein wrote about capturing an asteroid and changing its orbit in his still excellent short story Misfit:

Eighty-eight swung some millions of miles further around the sun. The pock-marks on her face grew deeper, and were lined with durite, that strange close-packed laboratory product which (usually) would confine even atomic disintegration. Then Eighty-eight received a series of gentle pats, always on the side headed along her course. In a few weeks' time the rocket blasts had their effect and Eighty-eight was plunging in an orbit toward the sun.

When she reached her station one and three-tenths the distance from the sun of Earth's orbit, she would have to be coaxed by another series of pats into a circular orbit. Thereafter she was to be known as E-M3, Earth-Mars Space Station Spot Three.
(moving an asteroid)