@Karl Katzke is correct that this is allowed in NEC 2008 code, but it is not allowed according to NFPA 2009 code. @Joe is correct that NEC 2011 has made changes to the code introducing sections 770.113(B), 800.113(B), 820.113(B) and 830.113(B) to match more closely to NFPA standards.
Personally I would try to avoid it if at all possible, if only for the simple fact that you'll likely be punching holes in the vents that will need to be properly sealed. You'll also have to worry about the cable if/when you have the ducts cleaned.
This will also depend on the codes that your local area follows, so you'll want to check with your local government.
National Electrical Code 2008
300.22 Wiring in Ducts, Plenums, and Other Air-Handling Spaces.
(B) Ducts or Plenums Used for Environmental Air. Only wiring methods consisting of Type MI cable, Type MC cable employing a smooth
or corrugated impervious metal sheath without an overall nonmetallic
covering, electrical metallic tubing, flexible metallic tubing,
intermediate metal conduit, or rigid metal conduit without an overall
nonmetallic covering shall be installed in ducts or plenums
specifically fabricated to transport environmental air. Flexible metal
conduit shall be permitted, in lengths not to exceed 1.2 m (4 ft), to
connect physically adjustable equipment and devices permitted to be in
these ducts and plenum chambers. The connectors used with flexible
metal conduit shall effectively close any openings in the connection.
Equipment and devices shall be permitted within such ducts or plenum
chambers only if necessary for their direct action upon, or sensing
of, the contained air. Where equipment or devices are installed and
illumination is necessary to facilitate maintenance and repair,
enclosed gasketed-type luminaires shall be permitted.
Which means, NO. The only wiring allowed in ducts, is wiring that is "necessary for their direct action upon, or sensing of, the contained air.".
Mike Holt explains it well in this YouTube video.
If you read article 725, you'll see that it references back to section 300.22.