Round-robin is a tournament system where every player plays against every other player. Usually each player meets each other player only once, but sometimes players meet twice, once with black and once with white. This is also called "double round-robin".
Round-robin is often used in league systems, where the leagues contain a limited number of players or teams. It is not generally feasible for large groups, as the number of games required is then too large.
The European Team Championship uses a league format as of 2010.
For a method to easily pair any number of players, see Easy Round Robin Pairing.
Example (6 players):
Number the players. For the first round arrange them in a folded pattern.
1 2 3
6 5 4
This means that player #1 plays player #6, #2 plays #5, and #3 plays #4.
For the next round, have player #6 remain stationary ("pivot player") and the other players move one seat clockwise. Once the movement is complete, players facing each other are paired for that round.
5 1 2
6 4 3
Repeat till players #2 through #5 return to their original seats. At that point the pairing have been completed, each player will have played five rounds. This simple method guarantees that each player plays every other player. :-)
In case of an odd number of participants, use a dummy player (make it the pivot player?).
Before the tournament make up 3x5 cards with the pairings on them for each player. The card for #1 will look like this:
The cards should have different colors (or other distinguishing marks) for different groups of 6.
Alternatively, make the first round pairings and then make up and post pairing sheets during the first round that people can refer to. I used to do that, using names rather than numbers. Making cards beforehand is easier if you want to play. :-)
Rounds do not have set time limits. People just find their next opponent.
A 6 person round robin makes for 5 rounds. In my experience, you can open registration at 9:00 a. m., start play by 10:00, break for lunch, and still finish in time for supper. A pleasant 1-day tournament. :-)
Of course, doing groups of 6 is not likely to produce a single winner, assuming you get a fair turnout. But does that matter?
SAS: (The Oxford Companion to Chess says that the term round-robin is "apparently based on a misunderstanding". Does anyone know more about this?) Phelan: This question was replied to in the talk page.
Free generator of round robin schedules and more: http://www.wjporter.com/chess_etc/rrpair.htm