The short answer is: depends.
There are multiple discussions on Airliners regarding the subject. One from 2004 and another from 2011.
General consensus is that it is not possible with few exceptions:
- Accompanying live cargo
- Being an employee of the company flying the cargo
- In the remote areas like Alaska it may be possible to be flying a half and half plane. Half cargo - Half passenger.
- You are an airline crew member or a courier in that case you can request a Jumpseat Service from cargo airlines like Atlas (maybe someone can enlighten me what Groom means here)
Save those you are likely to be denied access to the plane