Diseases caused by mutations resulting in toxic gain of function exist. Huntington's disease and some forms of ALS, for example. Generally these are inherited in a dominant fashion, since you only need one copy producing toxic proteins to mess things up.

For toxic gain of function mutations, there are various technologies for silencing the expression of toxic genes currently in clinical trials. Most of them use complementary RNA strands that bind to mRNA, preventing it from being used to synthesize proteins. I don't think any of these are currently FDA approved, but there should be some within a few years.

(Edit: According to Wikipedia, there are actually four RNAi (RNA interference) drugs on the market already).

Conversely, loss-of-function mutations are generally inherited in a recessive fashion, since one copy of a gene will usually produce enough of a protein. I believe that there are a handful of loss-of-function diseases inherited in dominant fashion due to haploinsufficiency (where one good copy cannot produce sufficient quantities of a needed protein).

There's some evidence that c9orf72 hexanucleotide repeat expansions, the most common genetic cause of ALS and FTD, involves both haploinsufficiency and toxic gain of function. Basically, the mutant c9orf72 protein doesn't fold correctly, producing toxic aggregations, and then there isn't enough good c9orf72 protein to clean up the mess. It's inherited in dominant fashion.