Yes, there are four moves that cover everything. In fact, you can have complete coverage with just two:
Ghost and Fighting.
If you think about it, Ghost covers all types at least normally effectively, except Normal and Dark (and Steel if you're on Gen V or earlier). Fighting covers all of these moves super effectively. The only way for these moves to lose their coverage is if Game Freak makes a Normal/Ghost Pokemon.
If you would like to know the four types that "have the least normal effectiveness," they are:
Ghost, Fighting, Ice, and Ground.
Not only do these types hit all types at least normally effective, but they hit super effectively on the vast majority of Pokemon: 588/774, to be exact.
I hope this answers your question.