Here is a list of games and contests that one could enter to play within RQ. Over at the design mechanism forums there is an excellent thread which mark.s started about how to play games within RQ6. He posted there rules for drinking games like Speed Drinking and Capacity Drinking. Among games of Skill and Prowess he has rules for Gwyddbwyll, Throwboard and Boasting Contest. Physical Games have Badger in the bag, Wrestling and Fire Jumping.
In Book of Quests by The Design Mechanism there are rules for pig wrestling. Trollpak has rules for Trollball – short version can be found here. Sun County has rules for Shield Push and in Garhound Contest in Sun County we have rules for Horse Race, Joust, Wrestling, Pain Test plus a full scenario built around them in Melisande’s Hand.
Gladiatorial contests and Chariot Races are covered in Monster Coliseum.