I think the most logical would have to water electric and ground. i cant really see another grouping that woulnt give one type an extreme advantage or disadvantage
Dark, Ghost and Psychic would be a cool match up, but I guess one isn't really all that weak against another. But it would make for a pretty awesome game IMO.
fighting, ice, and ground.. kind of boring... but these rock paper scizzors situations are hard to think of without stepping on toes. Also psychic dark and ghost wouldn't work because some attacks wouldn't even have any effect.