Actually, many competitors prefer that there is no formal definition of an adventure race - it lets organizers be more creative in providing new and different challenges. Here are some attempts we were able to dig up. Adventure races are self-sufficient races, through wilderness areas.
Navigation is always a requirement.
But there are plenty of interesting solo competitions also. The Eco-Challenge involves teams of five men and women navigating their way through remote wilderness areas 24 hours a day for up to 10 days. A team must not separate, and can only use natural means by which to travel. This may include horseback riding, rafting, mountain biking, swimming, paragliding, sailing, mountaineering, technical climbing, canyoneering, skiing, sledding, or any other challenge the organizers can think up. The course is kept secret until the start of the race, and the course and disciplines are revealed progressively as each team arrives at a transition area.