The short answer is: depends.

There are multiple discussions on [Airliners][1] regarding the subject.  One from [2004][2] and another from [2011][3].

General consensus is that it is not possible with few exceptions:

 1. Accompanying live cargo
 2. Being an employee of the company flying the cargo
 3. In the remote areas like Alaska it may be possible to be flying a half and half plane.  Half cargo - Half passenger.
 4. You are an airline crew member or a courier in that case you can request a [Jumpseat Service from cargo airlines like Atlas][4] (maybe someone can enlighten me what Groom means here)

Save those you are likely to be denied access to the plane

[1]: http://www.airliners.net
[2]: http://www.airliners.net/aviation-forums/general_aviation/read.main/2200932/
[3]: http://www.airliners.net/aviation-forums/general_aviation/read.main/5269089/
[4]: http://www.atlasair.com/aa/confirm2.html