Possible mechanisms fall into two categories:
4.1. Processes involving synchrotron-type emission from relativistic particles
The prime requirement here is an acceleration mechanism capable of channeling much of the energy into relativistic electrons. Acceleration mechanisms, though ill-understood, are known to be widespread, even in astrophysical contexts where conditions are far less extreme than in quasars. For instance it appears that decelerating supernova remnants such as Cass A have converted a few percent of their kinetic energy into cosmic ray particles. The most likely mechanisms involve either Fermi-type processes in shock fronts, or else field amplification via Rayleigh-Taylor instabilities which then permits efficient acceleration at neutral sheets. The velocities involved in supernova remnants are 10-2 c. When non-laminar accretion occurs onto a massive black hole, one expects shock waves near the hole (where most of the energy is released) to involve velocities larger than this; so whatever process operates in supernova remnants should occur even more efficiently. This is the most "conservative" class of acceleration mechanism. If relativistic blast waves  occur, then electrons can attain 1 by a "one-step" process, without the need for stochastic or Fermi-type processes across or behind the shock.
Some authors have considered magnetic flares in massive accretion disks - it is certainly plausible that much of the energy emitted near the hole, where orbital velocities may be ~ c/2, should go directly into relativistic particles, and eventually be radiated non-thermally.
A more exotic possibility has been explored by Blandford and Znajek , who have investigated the electromagnetic effects close to a black hole which accretes from a surrounding disk of plasma with a strong magnetic field. Even though the MHD approximation may hold in the disk (so that there is no E-field in a frame moving with the rotating matter), there may be insufficient plasma along the axis to short out an induced E-field. This E-field is limited by a vacuum breakdown whereby a single energetic electron (or photon) could initiate a shower of e+-e- pairs. This breakdown may resemble the Sturrock-Ruderman-Sutherland curvature radiation process originally proposed in the pulsar context, or could be initiated by Compton scattering of soft photons by high-energy electrons (and resulting pair production). For quasar parameters, one gets e+-e- pairs with Lorentz factor 106. This process in principle extracts rotational energy from a Kerr hole. This does not make much impact on the energy budget - a bigger contribution to comes from the gravitational binding energy of the infalling matter - but the hole's contribution is more likely to go directly into the "low entropy" form of ultrarelativistic particles which escape preferentially along the rotation axis. It may be relevant to note also that bulk expansion of an e+-e- plasma can attain higher Lorentz factors than an ordinary plasma, because in the latter case the ions provide greater rest mass. This is relevant to the interpretation of "superlight" velocities in radio components, discussed elsewhere in these proceedings.