If there is such thing as a "worst type", it's probably Normal. It's not super-effective against anything and Ghost is immune, and it is only immune to Ghost, and is weak to Fighting. There are plenty of great Normal-types, but their greatness lies not within their type. All of the good Normal-types would be better off as another type, and so would Normal moves. In fact, if every Normal-type move were Dragon-type, they would all be better because Steel already resists Normal, anyway.
But because there are so many good Normal Pokémon and moves, it's hard to call the type bad. That is why I do not think there is such thing as the worst type. Worst type combinations, probably, but not worst type in general.