Tournament Director for Windows use the Berger all play all chess pairing system.

Each of these generates different chess pairing combinations for all play all. The best known is the Berger system.

• Berger tables
  Berger pairings for tournaments with 3 to 30 players.
  
  

• Calculation for Berger pairings
  Berger tables for any number of players. Thisis an external link to the CERN Chess website.

• Cyclic and First Fit
   
• Polygon method
  
  

• Wikipedia provides more details about round robin pairings systems .