What do you like best?
Extremely quick. Easily customizable. Lots of shortcuts. Large community, Tons of templates.
What do you dislike?
Needs some polish when it comes the the user interface and shortcuts. There are also bugs, bugs, and bugs.
Recommendations to others considering the product
I would highly recommend Omnigraffle over most diagramming tools out there. I have tried many of them and in one way or another they have left me disappointed and have turned back to Omnigraffle. Once you learn how to outline with shortcuts the application becomes a breeze to use. Don't let the user interface deter you from learning this program. Take some tutorials and I guarantee you that you will never look back.
There are many useful stencils and templates that you can get for free to get you started. Once you have mastered how to use them it is very easy to start creating your own if you wish to. You can also import illustrator assets if you feel more comfortable creating vector assets in that program.
Omigraffle provides a range of export options as well so that you can produce jpegs, pngs, multiple page pdfs, and many more.
What business problems are you solving with the product? What benefits have you realized?
I am a user experience designer and I make diagrams, site maps, and user flows to realize client products. Omnigraffle is lighting fast. I am able to diagram a process during client meeting and have them approved by the end of the meeting. I also value the export options that allow me to produce artifacts for clients, managers, and developers.