Yes, double negatives can be okay. Sentences such as:
- There is no job I cannot do.
- I don't disagree with you.
- I have never not believed you.
are okay and easy to understand.
The "weird" ones:
- That won't do you no good
- She never goes with nobody
- You don't know nothing
- Baby, don't hurt me no more
are also okay, but they can be more tricky to understand.
The first kind of sentence ("there is no job I cannot do") is different from the second kind ("that won't do you no good").
In the first case, the double negative is used to mean a double negative. "There is no job I cannot do" means that out of all the jobs in the world, there are exactly 0 that I cannot do. "I don't disagree with you" means it is not the case that I disagree with you.
In the second case, the double negative actually means a single negative, and the double negative is used to make the negative stronger. "That won't do you no good" really means "That won't do you any good", or "That will do you no good". But by putting the two negatives together, the negative becomes stronger, and gives the sentence more emphasis.
For example, "baby, don't hurt me no more" might be more correct if it was "baby, don't hurt me anymore". But the word "no more" has a stronger sense of "no" to it, and it communicates a stronger emotional message.
This kind of double-negative used for a single-negative sentence is more common in some cultures, and is also used for stylistic effect (such as in song lyrics).