Below is a list of some of the most common golf game formats, some of which are used as competition formats at the St.Helena Golf Club.

Format
Description
Usual handicap allowed
Individual play formats  
Stroke Play Each stroke counts, including penalty strokes. Classic game.

Full handicap usually allowed (Except Open)
Medal Same as Stroke Play

 
Skins Each hole is worth one 'skin' and whoever wins the hole gets the skin. If no-one wins the hole outright then the 'skin' is carried over, so the next hole is worth 2 skins, and so on until someone wins the hole and the accumulated skins.

Play off scratch or handicap as per singles matchplay.
Stableford Points are awarded for a score on each hole on either a nett or handicap basis. 1 point for a bogey, 2 for a par, 3 for a birdie, 4 for an eagle, 5 for an albatross!. Any score worse than a bogey counts as 0. Player with the highest total points wins the match.

Full handicap usually allowed
Medalford Combination of Medal play for the front nine holes and Stableford play the back nine holes. The total score is the the net stroke play score for the front nine, minus the Stableford points score for the back nine.

Full handicap usually allowed
Modified Stableford Points are awarded for a score on each hole on either a nett or handicap basis. -1 point for a bogey, 0 for a par, 2 for a birdie, 5 for an eagle, 8 for an albatross!. Any score worse than a bogey counts as -1. Player with the highest total points wins the match.

Full handicap usually allowed
Par 3 Normal stroke play game, but where each hole is shortened to be a Par 3 hole. The course layout may be rearranged as a consequence, so new green approaches are common.

Decided by committee
Match Play Each hole counts one point for the player who wins it, and half a point for each player if the score is tied for the hole. Play continues until one player leads by more points than remain to be won.

Full handicap usually allowed
Bogey A Match Play format game played against a fictitious player (the Bogey) who always makes Par on every hole. For each hole, the player's score is modified by his handicap for that hole (respecting the Stroke Index ordering), and the hole won, lost or drawn accordingly. All holes are played, however, and the player's final score is a plus (up) or minus (down) number or zero (all-square).

Full handicap usually allowed
     
     
Team play formats *  
Foursomes Two teams of two, each team playing with one ball, where each player in a team plays a stroke alternately. Team players also alternate playing the drive off the tee. Otherwise the game is a standard Match Play game.

Team handicap is half the combined team players' handicaps.
Greensomes As for Foursomes, except that both team players take a drive and the team chooses which ball to continue the hole with. The weaker team has seven-eighths of the difference between the combined handicaps of each team. The stronger team plays without handicap.

Fourball Two teams of two, each player playing ther own ball as normal for the entire hole. The team scores the aggregate of the two players' net scores.
Each player's handicap is the difference between his normal handicap and that of the lowest handicap. (The lowest handicap therefore plays off scratch)

Fourball-Betterball Two teams of two, each player playing ther own ball as normal for the entire hole. The team scores the better of the two players' scores for each hole. Each player's handicap is three-quarters of the difference between his normal handicap and that of the lowest handicap. (The lowest handicap therefore plays off scratch)

High-Low Two teams of two, each player playing ther own ball. A point is awarded to the team with the lowest of the two team's lowest scores and similarly a point is awarded to the team with the lowest of the two team's highest scores. No point is awarded for a tied score.

Full handicap usually allowed
Four-ball Multiplier Stableford game for two teams of two. The team score is the product of the two players' Stableford score on each hole. (i.e. the Stableford scores are multiplied together).

Full handicap usually allowed
     
     
Fun formats  
Texas Scramble Two teams of two (or more), each player playing ther own ball. For each stroke, the team chooses which is the better ball, and both players play their next shot from the same spot.

Team handicap is one quarter of the combined handicaps of the team players' normal handicaps.

Tombstone Each player plays as many holes as possible using an allotment of strokes, and "dies" when the allotment is exhausted, including in the middle of a hole. The allotment is usually based on the player's handicap. The winner is the player who plays the furthest distance.

Full handicap usually allowed
Cross Country Normal stroke play game, but where the tees and greens have been rearranged to form a different course. Decided by committee

 

* Most team play formats can be played team-against-team (e.g. Fourball-BetterBall), or team-against-all-teams (e.g. Twoball-Betterball)