Multi event scoring system
You could consider a scoring system similar to those used in decathlon events. This would require significant thought prior to the event and a reasonable mathematics knowledge, but would provide a very tuneable system (if similar events are planned or if there's an expectation that some players may not reach some of the games).

A more basic version that works very well if all scores are "higher better" is to allocate a specific number of points to first place in every game, say 100. The remaining players receive points based of their score out of the winner's score, times the winner's points. This ensures an event with very close results will not unbalance the overall leaders, but that extreme performance in an event won't be discounted either.

For inspiration, here are some points-based systems and discussion:


Formula 1, high-performance racecar competition.
Decathlon, multisport Olympic event. This calculator by Decathlon2000.com may help, or if you want to develop your own system, the discussions there and at NRICH will be of great use.
This answer describes a "bottom-up" scoring system. While focused on a long-term repeated game, is also suitable for accumulating multiple games into one event. Combining this with other methods to encourage better performances would be no harder than developing a "top-down" system, and allows for a widely differing number of participants in each game.