It is hard to estimate how many people have tried Bochs or use it on a regular basis, but a few statistics give an indication. The bochs-developers mailing list, which is the primary source of news on bugs and releases, has over 400 subscribers. The latest version has been downloaded over 150,000 times from SourceForge, not counting any mirror website or GitHub users.
Bochs has many possible uses, and different people use it for different things. Many people use it to run applications in a second operating system without needing two different computers or dual-booting. Running Windows software on a non-x86 workstation or on an x86 Unix box are common uses. Also, because every hardware instruction and every line of simulator code is accessible, Bochs is used extensively for debugging new operating systems. If you were writing boot code for your home-brewed x86 operating system and it didn't work right, booting it in Bochs could give you great visibility into what is really going on. The Bochs debugger lets you simulate quickly or slowly, pausing whenever you want to look at the contents of memory or the CPU registers. Or, if you wanted to study which parts of a program take the most time, you could use Bochs to measure how often certain pieces of the code were executed.
Bochs has been used as a teaching tool in Operating Systems classes, in which students used and modified it to learn how the PC hardware works. As a final project the students had to add a new peripheral device, so they had to learn all about I/O ports, interrupts, and device drivers. In industry, it is used to support legacy applications on modern hardware, and as a reference model when testing new x86-compatible hardware.
There may be as many uses of Bochs as there are users. Do you want to run your old DOS games? Or learn how to program under GNU/Linux, without leaving your Windows desktop? Or reverse engineer your printer driver? You decide.