There are no longer any types without any weaknesses as of generation 6, but there are a handful of dual types that still have only one weakness:
- Ghost / Dark (has a x2 weakness to fairy)
- Poison / Dark (has a x2 weakness to ground)
- Water / Ground (has a x4 weakness to grass)
- Bug / Steel (has a x4 weakness to fire)
There is another dual type with only one weakness: Normal / Ghost, its only weakness being dark type. Since normal-ghost also has 3 immunities being ghost, normal, and fighting type, I would say Normal-Ghost type Pokemon are the best dual typed Pokemon. The problem is there aren't any!
There is also a chart on this very site, giving the cumulative scores of the lowest scoring dual types down the left side of the page, the lower the better. The winner of this competition is Steel-Fairy, and closely followed by Steel-Flying, with a score of 13.25 and 13.50 respectively. (This is explained in more detail if you follow the link.) Both of these type have two x2 weaknesses, but they both have a lot more resistances. So I would say the ultimate dual type is Steel-Fairy, but your opinion may be different.
Hope I helped!