What do you like best?
The simple interface makes getting a server up and running so simple. A click of a button gets your Apache and MySQL servers running, and then you've got a folder where all your 'sites' can live. Everything is customizable, so if you're more familiar with server stuff, then you can set it up however you like. But if you're not, MAMP make it really easy to get your site up and running locally.
What do you dislike?
It's an extra app to have loaded on your machine. There's not much to dislike, it's a simple product that does what it's supposed to really well. I'm sure if you're more server-savvy, then this might be a bit basic, but for us front-end devs, it's pretty sweet.
Recommendations to others considering the product
Use this if you're not super comfortable with servers in general. Really easy to set up and use, and if you are more server-savvy, all of the settings are customizable, just like any other type of server.
What business problems are you solving with the product? What benefits have you realized?
I use MAMP daily. All my sites in development run on it, as well as any sites that are getting updated. Simple, easy to use, would recommend for simpler sites.