I can think of a few off the top of my head: Charitable organizations, voting, and the gambling industry.
Why? Well, with regards to charitable organizations, I would personally love to see where my dollar(s) go with respect to the donation. So far as good faith goes, I (we) truly don't know where our money goes after donating. How much of that is paid to employees, executives, company, and how much of it reaches its intended location? Here are some large-scale examples from charity fraud/scandals in 2016. There needs to be higher levels of transparency and trust within these organizations, and utilizing the blockchain could be enormously beneficial.
I do believe that this same logic applies to voting- although staff and employees should of course, be trained, there must be large amounts of clerical error, worldwide, when counting the votes. Additionally, how much of a traditional voting system is susceptible to fraud?
Lastly, an interesting and perhaps even controversial one could be the gambling industry. There are massive amounts of trust issues when it comes to gambling- the fairness of the outcomes, the trust required from the player, the accuracy of random number generation, the centralization, etc. I think that with the trustless nature of blockchain and smart contracts, a lot of this could be solved- creating a safer space for players.
Note, I haven't named any particular company because the nature of my inquiry is regarding the industries in which blockchain could actually be useful. If you find a company that is tackling these sorts of things, without taking the word blockchain and using it as a marketing initiative, I'd love to hear about it.