Can Romex (NM-B) cable be run through conduit?
Yes, NM cable can be in conduit. In fact. NEC calls for it to be in conduit, when protection from physical damage is required.


  National Electrical Code 2011
  
  ARTICLE 334 Nonmetallic-Sheathed Cable: Types NM, NMC, and NMS
  
  II. Installation
  
  334.15 Exposed Work. In exposed work, except as provided in 300.11(A), cable shall be installed as specified in 334.15(A) through (C).
  
  (B) Protection from Physical Damage. Cable shall be protected from physical damage where necessary by rigid metal conduit, intermediate metal conduit, electrical metallic tubing, Schedule 80 PVC conduit, Type RTRC marked with the suffix -XW, or other approved means. Where passing through a floor, the cable shall be enclosed in rigid metal conduit, intermediate metal conduit, electrical metallic tubing, Schedule 80 PVC conduit, Type RTRC marked with the suffix -XW, or other approved means extending at least 150 mm (6 in.) above the floor. [ROP 7-94] Type NMC cable installed in shallow chases or grooves in masonry, concrete, or adobe shall be protected in accordance with the requirements in 300.4(F) and covered with plaster, adobe, or similar finish.


There's also some notes in Chapter 9, dealing with how to figure for cables when calculating conduit fill.


  Chapter 9 Tables
  
  Notes to Tables
  
  (5) For conductors not included in Chapter 9, such as
  multiconductor cables and optical fiber cables, the actual
  dimensions shall be used.
  
  (9) A multiconductor cable, optical fiber cable or flexible cord of two or more
  conductors shall be treated as a single conductor for
  calculating percentage conduit fill area. For cables that
  have elliptical cross sections, the cross-sectional area
  calculation shall be based on using the major diameter
  of the ellipse as a circle diameter.


However, it depends on where the conduit is.  If the conduit is underground (or any other damp or wet location), then NM cable is not allowed. 


  National Electrical Code 2011
  
  ARTICLE 300 Wiring Methods
  
  I. General Requirements
  
  300.5 Underground Installations.
  (B) Wet Locations. The interior of enclosures or raceways installed underground shall be considered to be a wet location. Insulated conductors and cables installed in these enclosures or raceways in underground installations shall be listed for use in wet locations and shall comply with 310.10(C). Any connections or splices in an underground installation shall be approved for wet locations.
  
  300.9 Raceways in Wet Locations Above Grade. Where raceways are installed in wet locations above grade, the interior of these raceways shall be considered to be a wet location. Insulated conductors and cables installed in raceways in wet locations above grade shall comply with 310.10(C).
  
  ARTICLE 334 Nonmetallic-Sheathed Cable: Types NM, NMC, and NMS
  
  II. Installation
  
  334.12 Uses Not Permitted.
  (B) Types NM and NMS. Types NM and NMS cables shall not be used under the following conditions or in the following locations:
  
  (4) In wet or damp locations