We usually base the format depending on how many players we have. If it's just our regular foursome, we typically play 2-man best-ball. In fact - that's the usual game most weekend rounds. It keeps play moving and in those occasional situations where a teammate is struggling - time isn't wasted with him continuing to play to score a double bogey or worse if his partner is virtually certain to have a lower score.
There are times however when we've got four pretty decent players and 2-man best ball can seem a little uneventful. That's when we might consider playing high and low. In this game each hole offers 2 points - a point for the low one-ball score, then another point for the low team total for the hole. Example: on a par4, player A for team one has a net par for the hole, player B has a net bogey. Player A for team two has a net birdie, but his partner has a net double. The one point would be awarded to team two for the low (birdie) but the other point is halved because obviously the teams both required the same amount of strokes to play the hole. So only one of the two available points are awarded in that situation.
Back when we had two or more groups, we'd occasionally play a "Miami" team match. For instance: you've got two teams of four players (ideal, although it can also be reworked for two teams of three players). The teams are usually made up comparably as far as overall team handicap totals, to keep the match somewhat fair and evenly matched. But we still award each player his full handicap nonetheless.
In our Miami matches we have three 6-hole matches. On the first 6-hole set, only the two lowest net scores of the four count for the team total on each hole. On the second 6-hole set - three of the four players scores count for each hole, and on the last set - all four scores are counted. We typically use stableford scoring system to keep things easier to track and tally. So if the lowest two net scores on the opening hole are pars, the team is awarded 4 points total for that hole, for example. So you have three 6-hole matches, then the overall match for the combined team points for all 18 holes. It sounds complicated but it really isn't. And what I've found normally is that the last 6-hole set (where every ball is counted) quite often is the difference maker in the overall.
Every now and then I would change the Miami format based on just one overall match, but using a similar concept. On all par3's - all four balls count. On all par4's - two balls count. On all par5's - only one ball counts. But again - the Miami format only works with an even number of players in two or three groups of 3 or 4 players each.
Sometimes we end up having only three players. When this happens we usually play 9's. There are 9 points up for grabs on each hole, based on your individual score versus the other two players. Each point is awarded a monetary value, usually a quarter or maybe 50 cents. Example: player A makes net par, player B makes net bogey, player C makes net birdie. Player C earns 5 points, player A earns 3 points, and player B earns 1 point. Sometimes we will award gross birdies with an additional point, depending on the terms of the match ahead of time... the guys I usually play with enjoy having the incentive of being rewarded for making birdies, above and beyond whatever the match might be, so we decided to add the birdie bonus for this game too.
There's one other 2-man best-ball format that we occasionally play too, particularly if we're playing with someone who doesn't play as often as we do, or might be going through a tough patch in his game. We obviously want to include everyone in the match, regardless of how he's playing or his overall skill level. It's called C.O.D.
COD is just two-man better ball, but the teams change every six holes. So there are three 6-hole matches. The first 6-hole match is cart versus cart. The next 6-hole match is opposites - the driver from one cart is teamed with the passenger from the other cart. The final 6-hole match is the drivers from both carts versus the passengers. We've found that this is probably the fairest and most practical way to conduct a team match with a weaker player, or perhaps just a way to change things up to keep things interesting.
We've played Wolf before too... it's okay, but not a huge fan really. There's also Vegas, which can be fairly complicated to explain and can also get quite expensive. If anyone is interested to know how Vegas works, I'll explain later.