What do you like best?
Damn faster, much handier and super powerful! This is the main reason pop out of my head first, let's break it down into smaller ones below.
First, less arm movement. So no more arm movement when we need to switch from the alpha keys to navigation keys (up down, home end ..) and modification keys (delete, backspace, insert ..), all can be done with your hands stick to the main section of the keyboard. We don't even need the mouse to scroll up/down, click, and navigate around. IMHO, tiny movements like that will slow you down a lot in your everyday typing life.
Handy key-strokes, and code-aid features, very friendly to coder. I was familiar with Eclipse and a few other code editors with very useful shortcut keys, and I can say, with a big help from various useful plugins, there's really nothing other editors have but vim doesn't, but NOT vice versa.
Plugins, a ton of it. A cool page to find one is http://vimawesome.com (we also have color theme there), or a classic one at http://www.vim.org/scripts . To be honest, there's a few plugins I find essential (such as NERDTree, Vundle ..) and actually keep thinking they are parts of vim itself. Plugins give vim value-added features, and some can be found in no other editor/ide.
(Finally, as it's too long already) Customizable, and pimp it your self. It's much like Arch Linux, comes initially with just the powerful core working instance, and everything else should be installed, customized based on your own need. So it may not always the best choice for no-i-dont-like-tweaking-anything guys.
What do you dislike?
Nothing, to be honest, but maybe, the learning curve, as it seems to be crazy to get started with vim, as it's different from most of the normal editors.
From what I've seen so far, as I recommended vim to a lot of people, there are only 2 types. The 1st, about 80% of people, will give up right in the first week, and never come back to try it again. The 2nd will never be able to happily code without vim after that damn hard first week. Once your muscles get used to it, you can never leave it.
Recommendations to others considering the product
Highly recommended, especially for new users who haven't found their ideal editors yet. To get started with it, `vimtutor` might help, and after that, you may grab an existing `.vimrc` (vim config) somewhere to see how people use vim in real life; mine could be found at https://github.com/soyelmnd/.swissknife . And as I'm a vim mania always wanna meet vim friends, feel free to drop me an email if you have troubles getting started with this damn cool weapon :-)
What business problems are you solving with the product? What benefits have you realized?
Everyday developer life, improve speed and productivity, a lot!
If I have to switch to another IDE, chances are I'll have to look for a way to enable vim-binding for that IDE (as I did with VRapper for Eclipse, Vimderbar for Brackets, and in Netbean), as typing without vim is a nightmare to me.