I'm rather keen on Water, Flying, as Psychic Types. Flying seems to be my favorite of the three.
Even though I thought before that the types that we have now are fine as-is, now I see that they aren't totally fair. Everybody's bound to have a fighting and dark type on their team, but nobody really wants a poison type.
I think the normal type is good as-is. Some normal types, like Kecleon and Castform, don't retain normal as their type while others like Granbull and Clefable have a large palette of moves to choose from. It's one of the "pros" to that type.
I had this idea initially that all Ghost types should be immune to all physical attacks and Dragon types would be either immune or resistant to special attacks. Then came the day I realized that Giratina was both Ghost and Dragon, so that kind of destroyed that.
Psychic pretty much covers all outer-space types. Deoxys, the Metagross family, and the Bronzor family are all psychic, and I don't know what kind of galaxy moves you would have a Clefairy family member learn.
If Pokemon had to add on more types, I'd say a Light type to defeat ghost, dark, and possibly water (water is such an abundant type, yet it has less weaknesses than grass and fire). Take that, Wonderguard Spiritombs! As far as weaknesses go, light-types should be weak against psychic and dragon types so then psychic can get back into the game and dragon now poses a type threat beyond itself. Pokemon such as Meganium (Typhlosion and Feraligatr also need a secondary type, Ground and Fighting or Dark, respectively), Bellossom, Sunflora, the Togepi family, the Swablu family, Illumise/Volbeat family, Pikachu family, Marill family, Plusle/Minun family, Pachirisu and its forecoming evolution, Finneon family, Mew (Mewtwo will get a second type, Dark), Manaphy and Phione, Cresselia (Darkrai would get Ghost as a secondary type), and Shaymin in its land form.
Sound is a possibility. There is just barely enough Pokemon to make this type possible, such as the Whismur family, Jigglypuff family, Chatot, Yanma family, Chimecho family, Kriketot family, Politoed, and possibly the Voltorb family. But I don't think this would make for a competitive type, I can only imagine a strength against ground types and weakness against flying.
The other type, which they kind of already have, is the "???" type. Unown would have that as a type (instead of Psychic), along with usually normal type Pokemon that don't stay normal usually in battle like Kecleon, Castform, Ditto, and Arceus without a plate. It would neither be strong nor weak against any type.