What do you like best?
The best thing about GNU Make is how it integrates with the user's installed shell commands and applications. This makes it great to write batch processing scripts for all sort of tasks, beyond just compilation automation. It also makes automatic timestamp checking of produced files so that it doesn't have to repeat steps unnecessarily. It also has support for parallel execution of tasks.
Also, it's command language is simpler than Microsoft's BAT and other shell script formats, a plus for writing scripts manually.
Since GNU Make (and UNIX make tool by extension) are old and time-tested tools there is also lot's of support for it, with things like libtool, automake and Cmake helping with the generation of makefiles for complex compilation workflows.
What do you dislike?
It's an integral part of the UNIX compilation workflow so using it outside of UNIX systems (namely Windows) is complicated. There are alternatives like Mingw32-make and Cygwin that attempt to solve this problem, however.
Recommendations to others considering the product
Take some time to practice it a bit if you want to use it manually. Also I recommend learning make before learning other related tools like CMake or the autoconf, automake, libtool combo. Even if you don't ever write a line of a Makefile yourself it pays to know how to read one for debugging purposes.
What business problems are you solving with the product? What benefits have you realized?
I use GNU Make personally to automate all sort of processes that produce intermediate files. Almost all my C/C++ projects use GNU Make (unless the size of the project is so small that adding Make becomes unnecessary).
I also use GNU Make to automate LaTeX compilations when writing technical reports and whitepapers.
I have even used it to compile Java projects using the LeJOS libraries for the LEGO Mindstorms robots since GNU Make is WAY easier to setup and use than Ant.