There are two kinds of golf tournaments; ones where everyone is serious about their final score and tournaments in which everyone is just out to have fun. These games are for golfers who put the emphasis on fun.
Lowest Putt Count
Have each player keep track of the total number of putt he takes for the entire round. Then choose random holes for which the putts will be counted. Choose as many holes as you like, but keep the hole numbers secret from the tournament field. Not knowing which putts will be counted can make for an interesting competition. For ties, use a tiebreaker such as lowest overall score or lowest total of putts.
Random Best or Worst Hole Score
Tournament games that use random criteria are always fun. Choose one hole on the front nine and one on the back nine. The person with the lowest combined score for the two holes is the winner. Use best total score as the tiebreaker.
Lowest Combined Score
Take the lowest combined score for the par 3s, or the par 5s and declare a winner for each. Or choose a stretch of three holes and use the combined score of those holes. The tiebreaker is lowest overall score.