What do you like best?
Hop helps to cut out all the clutter of signatures and previous emails while allowing you to see all the conversations you had with someone in the past in a simple view. So it helps reduce the amount of time spent on email. Hop works faster then any email client, and I have tried every one that I could find! The Priority Inbox vs Other inbox saves a lot of time sorting what is important and not important. If others are using Hop as well, it creates a realtime chat between each other. It also allows for encrypted messages between users, which is great when sending sensitive information.
What do you dislike?
Not much, would like a few other small features like Auto Snoozing, and location based reminders. But really, they have the best email client, and now that desktop will be available, it will be the best solution on your smartphone, tablet, and desktop.
Recommendations to others considering the product
If you want a simpler email, then use Hop. Some of the UI takes a little getting used to, and it starts in People organized mode, but you can change it back to the typical Inbox setting if that works better for you, which is what I do now. No reason not to try Hop at least for a month or so.
What business problems are you solving with the product? What benefits have you realized?
Hop allows for clearer communication and saving time spent on email. Allows for better context with a previous contact as well. I have saved a lot of hours on email, and a better experience then browser based email, or any other app.