What do you like best?
Our product requires quite complex prototyping, as it is too time consuming to iterate the actual product in many cases.
Axure provides a huge array of technical features that allows us to create those complex prototypes. By which I mean very particular functionality - the tools are flexible enough to create almost any behaviour, just by the fact that you can replicate programming logic (but you don't need to be a programmer!)
It's easy to achieve desired layouts and interactivity, you can nearly always replicate the intended design (even visually, if you need a realistic prototype rather than a wireframe).
Axure's sharing service is also incredibly useful; we use this to share among the team and to customers for testing.
What do you dislike?
The user interface is a bit dated, it works, it's usable but it's not exactly a pleasure to use. Some things could bit a bit slicker; it would be nice if the interactions panel was a bit less fussy, but to be honest I'm looking for faults.
Recommendations to others considering the product
There are quite a few prototyping tools on the market now that I have never used, so my review isn't a comparison with those other platforms. I think newer applications are more modern, but from what I know, nothing is as comprehensive as Axure in terms of functionality.
What business problems are you solving with the product? What benefits have you realized?
It also gives us a way to share prototypes very easily for user testing and team/customer reviews.